Can I publish client ID?
Technically, it should be okay.

Is it ok to push code with the Client ID in it?

The question you should ask yourself is, what information does the client ID give away? According to the Microsoft identity platform and the OAuth 2.0 client credentials flow a client_id is,

The Application (client) ID that the Azure portal – App registrations experience assigned to your app.

It is essentially like your name. It won't be end of the world if you give it away but you probably should not where there is no reason to.
Quoting, Should the OAuth client_id be kept confidential?

Your client_id is like your username or e-mail address you use to authenticate your application/service to OAuth. It's not exactly top-secret, but putting it out in the public domain might also be undesirable.

Further,

Can someone else use my Client ID?

Yes, but even in the confidential client apps, "The client ID is exposed through the web browser."
Note that we can actually see the Thunderbird's client id exposed in their source code. It isn't really meant to be private information.

If I can't safely push this to a public GitHub, how do I handle it?

You can use a password manager if you are the only user of your extension.

I've coded beyond my ability and managed to get MSAL authentication working for my Browser Extension. I'm ready to push code to GitHub.
Is it ok to push code with the Client ID in it? Can someone else use my Client ID? If I can't safely push this to a public GitHub, how do I handle it?
// Microsoft Authentication Library (MSAL) instance
// Client ID is the Application (client) ID GUID from the Azure portal
const msalInstance = new msal.PublicClientApplication({
    auth: {
        authority: "https://login.microsoftonline.com/common/",
        clientId: "ffffffff-ffff-ffff-ffff-ffffffffffff",
        redirectUri: redirectUri,
        postLogoutRedirectUri: redirectUri
    },
    cache: {
        cacheLocation: "localStorage"
    }
});

