Can I say X causes Y if all confounding factors are accounted for? Say I wish to understand the causal relationship between some set of covariates X and an outcome of interest y given some treatment T. For example, this may be as simple as modelling the relationship between middle-aged diabetic patients of a given gender and a treatment on blood sugar levels. If I account for all confounding variables and add them into my set of covariates, and let's say I then observe a strong correlation between X and Y given T, can I then assume that X equipped with treatment T causes Y rather than merely concluding some association?

Yes, as long as the potential cause precedes the outcome, in the absence of confounding, association is causation. "In the absence of confounding" is a high bar to pass; this means all backdoor paths are blocked and all models used to do so are correct.
Closing all backdoor paths is a technical matter that essentially means all confounders have been adjusted for, no effects of the treatment have been conditioned on, and there is no measurement error in the treatment, conditioned variables, or outcome. It also means there is no inadvertent selection (i.e., selecting units into the analysis based on the outcome or treatment).
For an introduction, I highly recommend Elwert (2013), and for a textbook, I recommend Hernán and Robins' "What If". I also encourage you to browse the causality tag on this site, which contains many insights about causal inference.
