Would be nice if the teleporter had "Logistic requests" section - like chests, rockets and space platforms
It would be good to manage the requests/etc and supply easier with bots

Teleporters will both be requesting and providing items, which makes them a little trickier to implement in this regard, and may be more confusing for end users as well. It's probably simpler and better to just have provider and requester chests next to the teleporter that you can load and unload into.

I guess it could work in similar manner like rocket silos that can request and provide items same time?

Rocket silos request items from the local logistics network and provide them to the orbital platform. Items coming back down from the platform don't go through the rocket silo, so there's no issue with having to provide to the local logistics network, like you might want a teleporter to.

Sorry, the more I think about it the less I want to even try doing something like this.