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

cmd/resolve-state/main.go

@@ -55,7 +55,7 @@ func main() {
 	fmt.Println("Fetching", len(snapshotNIDs), "snapshot NIDs")
 
 	roomserverDB, err := storage.Open(
-		base, &cfg.RoomServer.Database,
+		base.ProcessContext.Context(), base.ConnectionManager, &cfg.RoomServer.Database,
 		caching.NewRistrettoCache(128*1024*1024, time.Hour, true),
 	)
 	if err != nil {