refactor: http request binding (#38971)

Better than before, still not good enough (more work can be done in the
future)

And add the missing error handling in the PrivateContext "bind"
middleware.

By the way, picked some "TrimSpace" changes from "fix: trim whitespace
from SMTP address and port - #38934" (fix #38926)

go.mod

@@ -6,7 +6,7 @@ toolchain go1.26.6
 
 require (
 	connectrpc.com/connect v1.20.0
-	gitea.com/go-chi/binding v0.0.0-20260414111559-654cea7ac60a
+	gitea.com/go-chi/binding v0.0.0-20260818211407-ac8602c87be9
 	gitea.com/go-chi/cache v0.2.1
 	gitea.com/go-chi/captcha v0.0.0-20240315150714-fb487f629098
 	gitea.com/go-chi/session v0.0.0-20260708011333-ebced8a7a2d6