feat: add strategy support to lite mode

[BorisP1234]

Add strategies to lite mode.

Draft because of four reasons:

• [x] Add docs.
• [x] Least-connection counter does not remove counts, when a player leaves.
• [ ] Least-connection counter does not "see" connections changing backends and messing up the counter. Edit: will not be possible to fix with current structure of gate lite.
• [x] Finish reviews

Co-author: @okeanosthedev