

I am not sure, but was not there a work profile app in fdroid (possibly by the name of shelter, have not used it for a long time though, so not sure). If is/was on fdroid, it is likely to be foss, and not have these things.
Also, unless the app has internet permisions, I would not worry much about it. Apps can send data even without internet permissions (by means of using a 3rd party, like gms (google play service) or something else), but if your app relies on some 3rd party app, i would not consider it safe to begin with.
edit: yes the app is called shelter - https://f-droid.org/en/packages/net.typeblog.shelter/
the app has not been updated for 1.5 years, but readme suggests that it is in a functional state, and just requires maintainance on newer sdks, which they suggest that they still provide. - https://gitea.angry.im/PeterCxy/Shelter. There issues do seem to be active (https://lists.sr.ht/~petercxy/shelter), so I would not worry about that either.
you can create a python virtual environment, and you do not even have to install python for that. you can install python in a user only mode, and then create a virtual environment (these can be made anywhere, so for example, your downloads or documents folder(assuming you are allowed to access these folders, you usually do)), script would have to be modefied a bit, but still doable. In case you need help for this, feel free to reply/message