I use RealVNC to communicate with a home server where I have some housewide apps and network storage. It's what's called a "headless" operation, meaning the PC is running but it has no monitor connected to it. RealVNC provides a capability like any remote access software, no different than what happens if you've ever gotten remote tech support. When you connect to that PC, you have a window with that PCs display, and your keyboard and mouse (or touchpad) provide input to that other PC.

There's a time lag for operations and screen refresh when using it. I'd say it's best suited for what I think of as server operations, not for normal use. You certainly could use it for simple programs, etc., Sound doesn't come across, just the screen image. You wouldn't use it for games or watching video, because of the lack of sound and slow screen refresh times.

My server is the central place for all files - photos, video, data files, etc. The network storage is accessible from all PCs and all local programs, so the remote access is simply to more easily setup and manipulate what's there.

It works across your home network, the internet is not involved. It's free, try it, see if it does what you're looking for.

There's lots of ways to accomplish that. It's really a question of if you're willing to pay for some off the shelf solution or want to invest the time to do it yourself.