Every company that I've worked with that provided models internally did so through LiteLLM and offered both Anthropic and OpenAI models so it was trivial to switch between them.
I like all the different comments in this thread saying that most companies do X, where X is a different answer from each person: LiteLLM, GitHub Copilot, Claude Code.
Most companies just get you a Claude team sub and maybe a couple of skills.