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

federationapi/routing/routing.go

@@ -65,9 +65,9 @@ func Setup(
 	servers federationAPI.ServersInRoomProvider,
 	producer *producers.SyncAPIProducer,
 ) {
-	fedMux := base.PublicFederationAPIMux
-	keyMux := base.PublicKeyAPIMux
-	wkMux := base.PublicWellKnownAPIMux
+	fedMux := base.Routers.Federation
+	keyMux := base.Routers.Keys
+	wkMux := base.Routers.WellKnown
 	cfg := &base.Cfg.FederationAPI
 
 	if base.EnableMetrics {