Sanity check - always-on machine + laptop with remote desktop

I'm looking for a new laptop as my current one is falling apart, and one option that seems quite tempting at the moment is getting a desktop machine, leaving it running away in the background, and then accessing it using remote desktop software from a laptop (or even tablet) most of the time. My logic is that I want a fairly decent device for programming on and occasional games, but I also want something portable that I can carry into every room of my flat. I've also been experimenting more with Tailscale and using my laptop as a remote development machine and my phone as a dumb terminal while traveling abroad, and that's worked fairly well, so I'm interested in how far I can take this concept. Plus the idea of also being able to use my main device as a small homelab is kind of appealing as well.

The plan would be:

• Framework Desktop sits somewhere at home and is on all the time. My wife has a Framework laptop that she's quite impressed with, I realise the value proposition for desktop computers is less given there's already so much possibility to configure and upgrade, but I've never built a PC myself before and I don't want to complicate this setup too much.
  '* A dumb terminal device that I can carry around with me. For now, that'll probably be my current laptop as long as it lasts, but in the future maybe a cheap Chromebook or even a tablet that I can connect a keyboard and mouse to.
• Moonlight/Sunshine setup for the remote desktop side of things. From what I can tell, this can stream both individual applications but also the whole desktop, and works with various clients.
• Tailscale to access all of this outside the home. This is less important but it would be convenient. And if I go down the homelab direction, also for being able to access my self-hosted services remotely or running my personal website off my own hardware.

Things I'm concerned about:

• German connection speeds are, broadly speaking, poor, especially with upload speeds. I'm looking at maybe 300M down, 50M up. Inside my local network that won't affect me, but if I did want to take my laptop with me, I don't have a good sense of whether the remote desktop aspect is really feasible.
• The Framework desktop - I like the company, and I like the idea of a repairable desktop that's still sold as a single unit and not something where I need to buy everything myself. But I also don't have a good sense of how much of a premium I'd be paying here, vs either building something completely from scratch or buying a more typical desktop
• The laptop would probably live in the living room because that's where all the other technology (in particular the modem) in our house lives. It's fine if it makes a noise while I'm actively using it to watch things, but I'd need it to be very quiet the rest of the time. Framework does sell a fan that is specifically designed to be quiet, but I'm not sure if this is "it's quiet compared to having a normal computer fan on" or "it's quiet compared to having turned all my devices off for the night".

Does anyone have any experience with this kind of setup, and is this something that would reasonably work, or am I completely missing something obvious that makes this a terrible awful idea that nobody should do?

Thanks in advance!