Is there an option to "use the remote computer just as it was local" even between two Macs? Sure, terminal/ssh is enough for most use-cases, but this is something I expected from Apple as builtin.
I can tailscale into my home network, but what next? VNC/TeamViewer/Remote Desktop setups are all mediocre imho.
I find Jump Desktop to be excellent. One time payment. Can connect from iPhone / iPad, too. A noticeable step up from Screen Sharing (which can’t be used from mobile device anyway). Can’t recall it ever failing to connect or flaking out as so many RDP setups seem to.
I once tinkered with the game streaming set up available via Steam, so I could do it in a way where it streamed the normal complete desktop setup. I used it to operate my desktop from the laptop.
It worked relatively well, but wasn't perfect. It was as close to what you're describing as I've seen, though. This was a few years ago; something like this might work even better now.
Apple Remote Desktop is very usable. I have a headless mini and have managed to fool myself about which machine I’m on, over WiFi.
Well, there used to be nxhosting back in the NeXT days, which I _really_ miss.
Unfortunately, it relied on Display PostScript and Quartz née Display PDF isn't architected to allow that sort of remote display/access on a per application level.
Unfortunately there is nothing that works as nicely as Windows Remote Desktop. Probably the best option is various commercial offerings as Apple Remote Desktop is rather buggy and unstable.
Astropad Workbench
Apple screen sharing works for me just fine. Matter of fact I have been driving a mac mini with it from my laptop most of the time now and just ordered a mac studio to replace the mac mini. I think powerful headless desktops are the future.