pkg/web: remove dependency injection (#49123)

* pkg/web: store http.Handler internally

* pkg/web: remove injection

Removes any injection code from pkg/web.

It already was no longer functional, as we already only injected into
`http.Handler`, meaning we only inject ctx.Req and ctx.Resp.

Any other types (*Context, *ReqContext) were already accessed using the
http.Request.Context.Value() method.

* *: remove type mappings

Removes any call to the previously removed TypeMapper, as those were
non-functional already.

* pkg/web: remove Context.Invoke

was no longer used outside of pkg/web and also no longer functional

pkg/api/common_test.go

@@ -411,10 +411,7 @@ func setupHTTPServerWithCfgDb(t *testing.T, useFakeAccessControl, enableAccessCo
 	m.Use(func(c *web.Context) {
 		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))