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/routing/routing.go

@@ -43,7 +43,7 @@ func Setup(
 	rsAPI api.SyncRoomserverAPI,
 	cfg *config.SyncAPI,
 	lazyLoadCache caching.LazyLoadCache,
-	fts *fulltext.Search,
+	fts fulltext.Indexer,
 ) {
 	v1unstablemux := csMux.PathPrefix("/{apiversion:(?:v1|unstable)}/").Subrouter()
 	v3mux := csMux.PathPrefix("/{apiversion:(?:r0|v3)}/").Subrouter()

syncapi/routing/search.go

@@ -37,7 +37,7 @@ import (
 )
 
 // nolint:gocyclo
-func Search(req *http.Request, device *api.Device, syncDB storage.Database, fts *fulltext.Search, from *string) util.JSONResponse {
+func Search(req *http.Request, device *api.Device, syncDB storage.Database, fts fulltext.Indexer, from *string) util.JSONResponse {
 	start := time.Now()
 	var (
 		searchReq SearchRequest