Preparations for removing BaseDendrite (#3016)

Preparations to actually remove/replace `BaseDendrite`.
Quite a few changes:
- SyncAPI accepts an `fulltext.Indexer` interface (fulltext is removed
from `BaseDendrite`)
- Caches are removed from `BaseDendrite`
- Introduces a `Router` struct (likely to change)
  - also fixes #2903
- Introduces a `sqlutil.ConnectionManager`, which should remove
`base.DatabaseConnection` later on
- probably more

syncapi/consumers/clientapi.go

@@ -50,7 +50,7 @@ type OutputClientDataConsumer struct {
 	stream       streams.StreamProvider
 	notifier     *notifier.Notifier
 	serverName   gomatrixserverlib.ServerName
-	fts          *fulltext.Search
+	fts          fulltext.Indexer
 	cfg          *config.SyncAPI
 }