I have a yaml file which is similar to the following (FYI: ssm_secrets can be an empty array):
rabbitmq:
  repo_name: bitnami
  namespace: rabbitmq
  target_revision: 11.1.1
  path: rabbitmq
  values_file: charts/rabbitmq/values.yaml
  ssm_secrets: []
app_name_1:
  repo_name: repo_name_1
  namespace: namespace_1
  target_revision: target_revision_1
  path: charts/path
  values_file: values.yaml
  ssm_secrets:
    - name: name-dev-1
      key: .env
      ssm_path: ssm_path/dev
name-backend:
  repo_name: repo_name_2
  namespace: namespace_2
  target_revision: target_revision_2
  path: charts/name-backend
  values_file: values.yaml
  ssm_secrets:
    - name: name-backend-app-dev
      ssm_path: name-backend/app/dev
      key: app.ini
    - name: name-backend-abi-dev
      ssm_path: name-backend/abi/dev
      key: contractTokenABI.json
    - name: name-backend-widget-dev
      ssm_path: name-backend/widget/dev
      key: name.ini
    - name: name-abi-dev
      ssm_path: name-abi/dev
      key: name_1.json
    - name: name-website-dev
      ssm_path: name/website/dev
      key: website.ini
    - name: name-name-dev
      ssm_path: name/name/dev
      key: contract.ini
    - name: name-key-dev
      ssm_path: name-key/dev
      key: name.pub

And using External Secrets and EKS Blueprints, I am trying to generate the yaml file necessary to create the secrets
resource "kubectl_manifest" "secret" {
  for_each   = toset(flatten([for service in var.secrets : service.ssm_secrets[*].ssm_path]))
  yaml_body  = <<YAML
apiVersion: external-secrets.io/v1beta1
kind: ExternalSecret
metadata:
  name: ${replace(each.value, "/", "-")}
  namespace: ${split("/", each.value)[0]}
spec:
  refreshInterval: 30m
  secretStoreRef:
    name: ${local.cluster_secretstore_name}
    kind: ClusterSecretStore
  data:
  - secretKey: .env
    remoteRef:
       key: ${each.value}
YAML
  depends_on = [kubectl_manifest.cluster_secretstore, kubernetes_namespace_v1.namespaces]
}

The above works fine, but I also need to use the key value from the yaml into secretKey: <key_value from yaml>.
If I try with for_each   = toset(flatten([for service in var.secrets : service.ssm_secrets[*]]))
resource "kubectl_manifest" "secret" {
  for_each   = toset(flatten([for service in var.secrets : service.ssm_secrets[*]]))
  yaml_body  = <<YAML
apiVersion: external-secrets.io/v1beta1
kind: ExternalSecret
metadata:
  name: ${replace(each.value["ssm_path"], "/", "-")}
  namespace: ${split("/", each.value["ssm_path"])[0]}
spec:
  refreshInterval: 30m
  secretStoreRef:
    name: ${local.cluster_secretstore_name}
    kind: ClusterSecretStore
  data:
  - secretKey: .env
    remoteRef:
       key: ${each.value["ssm_path"]}
YAML
  depends_on = [kubectl_manifest.cluster_secretstore, kubernetes_namespace_v1.namespaces]
}

It just gives me the following error:

The given "for_each" argument value is unsuitable: "for_each" supports
maps and sets of strings, but you have provided a set containing type
object.

I have tried converting the variable into a map, used lookup, but it doesn't work.
Any help would be much appreciated.
Update 1:
As per @MattSchuchard suggestion, changing the for_each into
for_each   = toset(flatten([for service in var.secrets : service.ssm_secrets]))
Gave the following error:
Error: Invalid for_each set argument
│ 
│   on ../../modules/02-plugins/external-secrets.tf line 58, in resource "kubectl_manifest" "secret":
│   58:   for_each   = toset(flatten([for service in var.secrets : service.ssm_secrets]))
│     ├────────────────
│     │ var.secrets is object with 14 attributes
│ 
│ The given "for_each" argument value is unsuitable: "for_each" supports maps and sets of strings, but you have provided a set containing type object.

Update 2:
@mariux gave the perfect solution, but here is what I came up with. It's not that cleaner, but definitely works (PS: I myself am going to use Mariux's solution):
locals {
  my_list = tolist(flatten([for service in var.secrets : service.ssm_secrets[*]]))
}


resource "kubectl_manifest" "secret" {

  count      = length(local.my_list)
  yaml_body  = <<YAML
apiVersion: external-secrets.io/v1beta1
kind: ExternalSecret
metadata:
  name: ${replace(local.my_list[count.index]["ssm_path"], "/", "-")}
  namespace: ${split("/", local.my_list[count.index]["ssm_path"])[0]}
spec:
  refreshInterval: 30m
  secretStoreRef:
    name: ${local.cluster_secretstore_name}
    kind: ClusterSecretStore
  data:
  - secretKey: ${local.my_list[count.index]["key"]}
    remoteRef:
       key: ${local.my_list[count.index]["ssm_path"]}
YAML
  depends_on = [kubectl_manifest.cluster_secretstore, kubernetes_namespace_v1.namespaces]
}


Terraform for_each over yaml file contents which is an object
Assumptions
Based on what you shared, i make the following assumptions:

the service is not actually important for you as you want to create external secrets by ssm_secrets.*.name using the given key and ssm_path attributes.
each name is globally unique for all services and never reused.

terraform hacks
Based on the assumptions you can create an array of ALL ssm_secrets using
locals {
  ssm_secrets_all = flatten(values(var.secrets)[*].ssm_secrets)
}

and convert it to a map that can be used in for_each by keying the values by .name:
locals {
  ssm_secrets_map = { for v in local.ssm_secrets_all : v.name => v }
}

Full (working) example
The example below works for me and makes some assumption where the variables should be used.

Using yamldecode to decode your original input into local.input
Using yamlencode to make reading the manifest easier and removing some string interpolcations. This also ensures that the indent is correct as we convert HCL to yaml.

A terraform init && terraform plan will plan to create the following resources:
 kubectl_manifest.secret["name-abi-dev"] will be created
 kubectl_manifest.secret["name-backend-abi-dev"] will be created
 kubectl_manifest.secret["name-backend-app-dev"] will be created
 kubectl_manifest.secret["name-backend-widget-dev"] will be created
 kubectl_manifest.secret["name-dev-1"] will be created
 kubectl_manifest.secret["name-key-dev"] will be created
 kubectl_manifest.secret["name-name-dev"] will be created
 kubectl_manifest.secret["name-website-dev"] will be created

locals {
  # input = var.secrets
  ssm_secrets_all = flatten(values(local.input)[*].ssm_secrets)
  ssm_secrets_map = { for v in local.ssm_secrets_all : v.name => v }

  cluster_secretstore_name = "not provided secretstore name"
}

resource "kubectl_manifest" "secret" {
  for_each = local.ssm_secrets_map

  yaml_body = yamlencode({
    apiVersion = "external-secrets.io/v1beta1"
    kind       = "ExternalSecret"
    metadata = {
      name      = replace(each.value.ssm_path, "/", "-")
      namespace = split("/", each.value.ssm_path)[0]
    }
    spec = {
      refreshInterval = "30m"
      secretStoreRef = {
        name = local.cluster_secretstore_name
        kind = "ClusterSecretStore"
      }
      data = [
        {
          secretKey = ".env"
          remoteRef = {
            key = each.value.key
          }
        }
      ]
    }
  })

  # not included dependencies
  # depends_on = [kubectl_manifest.cluster_secretstore, kubernetes_namespace_v1.namespaces]
}

locals {
  input = yamldecode(<<-EOF
    rabbitmq:
      repo_name: bitnami
      namespace: rabbitmq
      target_revision: 11.1.1
      path: rabbitmq
      values_file: charts/rabbitmq/values.yaml
      ssm_secrets: []
    app_name_1:
      repo_name: repo_name_1
      namespace: namespace_1
      target_revision: target_revision_1
      path: charts/path
      values_file: values.yaml
      ssm_secrets:
        - name: name-dev-1
          key: .env
          ssm_path: ssm_path/dev
    name-backend:
      repo_name: repo_name_2
      namespace: namespace_2
      target_revision: target_revision_2
      path: charts/name-backend
      values_file: values.yaml
      ssm_secrets:
        - name: name-backend-app-dev
          ssm_path: name-backend/app/dev
          key: app.ini
        - name: name-backend-abi-dev
          ssm_path: name-backend/abi/dev
          key: contractTokenABI.json
        - name: name-backend-widget-dev
          ssm_path: name-backend/widget/dev
          key: name.ini
        - name: name-abi-dev
          ssm_path: name-abi/dev
          key: name_1.json
        - name: name-website-dev
          ssm_path: name/website/dev
          key: website.ini
        - name: name-name-dev
          ssm_path: name/name/dev
          key: contract.ini
        - name: name-key-dev
          ssm_path: name-key/dev
          key: name.pub
    EOF
  )
}

terraform {
  required_version = "~> 1.0"

  required_providers {
    kubectl = {
      source  = "gavinbunney/kubectl"
      version = "~> 1.7"
    }
  }
}

hint: you could also try to use the kubernetes_manifest resource instead of kubectl_manifest
p.s.: We created Terramate to make complex creation of Terraform code easier. But this seems perfectly fine for pure Terraform.
