Is it inappropriate to use school-provided remote learning tools to pursue friendship or relationship with another student?
For already established contacts, there should not be any problem. Same when you ask a group of known and new people (e.g. the general group chat), whether they want to do something together (which might not be the best idea at the moment, but I hope you get what I mean).
Contacting specific people that are not your friends might be a different story, especially if your approach might not be desired. If you go this way I would be very careful in how you are approaching someone, especially if it is, or can be perceived as such, of romantic nature. One way to go could be to start out with asking if the other person is okay with being contacted by you for private matters at all in this system.
However, I would suggest to try social media instead. Or ask common friends/acquaintances for a contact - the way we did it before social media existed. Again, of course, nice and respectful.