Trainer Road does not sound like a good fit for your list. It's aimed at riders who want a fully managed interval training plan and nothing else.
Zwift is king for racing and group riding and the ERG mode and workout editor is actually pretty good. It is not bad for virtual climbing either, especially with the new climb portal function.
Rouvy is easily your best option for virtual climbing and it can tick off all your other boxes too. But racing and group rides are pretty limited compared to Zwift. You really have to plan ahead for those, while Zwift has rides and races 24/7 so you can just hop on and go.
I use both Zwift and Rouvy for variety. With Zwift you can pause your account at any time, which is useful if using multiple Apps.