>these modern social media and influencer versions of Stoicism feel like something else entirely

Yes, the pop philosophy folks tend to confuse Stoicism with Spartanism, just like they confuse Epicureanism with Hedonism. It also helps to have a basic understanding of ancient Aretaic (Virtue) Ethics and the context in which some of these works were written (e.g., was one work or school of thought developed in response to some other one that preceded it).

As always, it's best to read the original works, and in the case of the Stoics (Epictetus, Aurelius, Seneca) they're really not difficult reads assuming a decent modern translation.

Also stay away from the manosphere influencers who peddle the weird self help stuff you allude to, whether under the guise of Stoicism or anything else.