Make peeking not use deprecated endpoints

Peeking got implemented in a rush and uses `/initialSync` and `/events`, which are deprecated. We should either resolve to keep them for the special case of peeking, or figure out what to replace them with.

Start by reviewing the peeking behavior around the deprecated /initialSync and /events endpoints, along with the relevant Matrix specification sections. Resolve whether those endpoints should remain as a special case or identify their replacements; the work is done when the peeking endpoint usage is unambiguous and documented.

Written by the indexing model from the issue text.