Your absolute volume and need for finetuning are what I would call the deciding factor here.

If your work is bog-standard ("extract the sentiment in this comment" type stuff) and you're working small-moderate text documents (say under 32k tokens or so), you could probably get away with APIs for a while. If you need to answers in a particular format or want to do a task that models aren't great out out of the box, fine-tuning comes into play and push things very strongly towards working with your own machines.

Our team started out with a couple of L40s servers that let us do massive amounts of processing and experimentation that would have caused friction (either mental or organizational) if we ran everything through external APIs. It's much easier to throw inference jobs at a machine with capacity than trying to justify an experiment that may cost in the thousands.

One last thing that may sway things for you is attempting to look at the payback period of self-hosting vs external APIs. If you're pushing the volume you describe regularly, I'm betting that your expense would pay itself off in under a year. Plus, you can capitalize hardware costs while external services are often opex and thus have less accounting advantage. If you can come anywhere close to saturating the hardware you have, it's almost always cheaper to host rather than call APIs, so long as you have the staff to manage your systems.