pkg/web: restrict handler types (#48495)

Makes `pkg/web` only accept handles from the following set:

```go
	handlerStd       = func(http.ResponseWriter, *http.Request)
	handlerStdCtx    = func(http.ResponseWriter, *http.Request, *web.Context)
	handlerStdReqCtx = func(http.ResponseWriter, *http.Request, *models.ReqContext)
	handlerReqCtx    = func(*models.ReqContext)
	handlerReqCtxRes = func(*models.ReqContext) Response
	handlerCtx       = func(*web.Context)
```

This is a first step to reducing above set to only `http.Handler`.

---

Due to a cyclic import situation between `pkg/models` and `pkg/web`, parts of this PR were put into `pkg/api/response`, even though they definitely do not belong there. This however is _temporary_ until we untangle `models.ReqContext`.

pkg/api/common_test.go

@@ -27,6 +27,7 @@ import (
 	"github.com/grafana/grafana/pkg/services/auth"
 	"github.com/grafana/grafana/pkg/services/contexthandler"
 	"github.com/grafana/grafana/pkg/services/contexthandler/authproxy"
+	"github.com/grafana/grafana/pkg/services/contexthandler/ctxkey"
 	"github.com/grafana/grafana/pkg/services/dashboards"
 	dashboardsstore "github.com/grafana/grafana/pkg/services/dashboards/database"
 	dashboardservice "github.com/grafana/grafana/pkg/services/dashboards/service"
@@ -411,6 +412,9 @@ func setupHTTPServerWithCfgDb(t *testing.T, useFakeAccessControl, enableAccessCo
 		initCtx.Context = c
 		initCtx.Logger = log.New("api-test")
 		c.Map(initCtx)
+
+		c.Req = c.Req.WithContext(ctxkey.Set(c.Req.Context(), initCtx))
+		c.Map(c.Req)
 	})
 
 	m.Use(accesscontrol.LoadPermissionsMiddleware(hs.AccessControl))