It’s probably not so much that you are using one API for all three, but rather that they are all using the same offset parameter. If you give them their own offset, you should be able to control them distinctly.
And for what it’s worth, I see nothing wrong with three APIs, but they would still need separate offsets.
So this means on your API, your paged query actions are looking for a $_GET.offset.
You will need to split this into 3 different query parameters, and yes you can do that in the UI. Each of your server connection actions on the front end will point to its own query parameter. And then on your API, each of the queries, will be paired with one of the $_GET parameters.