Use client logger in more places (core code) (#4899)
* Use client logger for sync
Use the logger attached to the MatrixClient when writing log messages out of
the sync api. This helps figure out what's going on when multiple clients are
running in the same JS environment.
* Use client logger for to-device message queue
* Use client logger in `PushProcessor.rewriteDefaultRules`
* use client logger in `ServerCapabilities`
* Mark global `logger` as deprecated
