Sadly, not at all. Windows can connect to the phone through its Link with Windows app, but not every function is accessible. For example, you can’t access screen mirroring to a laptop.
Speaking for messages: I can’t say nothing as I’m not using it on PC, but the mentioned app has an option to view and, maybe, send messages. I guess, you can just install Google messages to PC so it will work as you described. With Samsung before I had an access to everything and even calls so I could answer the call on PC. I haven’t received any calls from Nothing while running a PC but I pretty sure it can also do the same. I see all notifications come from phone.
It’s not as good in sending files tbh, it crashes sometimes, so I’m just sending most of the stuff to my Favourites chat on Telegram as files🤷🏼♀️