Not strictly "out of the box" since the setting isn't enabled by default, but any distro with a recent version of GNOME installed will have RDP available. It's ready to be toggled on in settings under System > Remote Desktop > Desktop Sharing:

Unfortunately, RDP always seems to be fiddly for me, it does that disconnect immediately after connecting that you described. Sometimes if I just keep hitting connect over and over, eventually it'll get confused and stop disconnecting so that I can actually use the desktop for a while. YMMV.

KDE has KRDP, which has a KCM for KDE Plasma.

I might tick off some "rtfm" purists suggesting out of the box distros, but...

RPM Based I used Fedora KDE's wayland session for the longest and its rdp implementation seemed to work without issue through krdp/krdc. Universal Blue is a new-ish project built on Fedora that has "immutable" updates. Essentially, a backup is always created when you update, so if you break something you can just roll back. Also software by default doesn't have permission to modify system packages so you don't have to worry much about accidentally bricking your system. There's a couple images for U-Blue, Aurora and Bazzite. Bazzite is gaming focused, everything you might want is installed by default. Aurora, I haven't tried, but it seems to be workstation focused with a lot of software dev tools. Opensuse Tumbleweed is ok... I didn't stick on it as long due to fedora having a significantly larger software selection at the time, but KDE on there had just as robust a rdp solution as well.

Arch Based There's Arch, it works. Been a few years since I used it, but there's the extensive documentation. I referenced it heavily whenever I wanted to do something system breaking for aesthetic purposes. But, it's definitely not out of the box and requires reading the manual. EndeavorOS seems like it makes the Arch experience not-painful but I haven't used it longer than a day. CachyOS seems promising as an out of the box solution, I haven't tried it yet but I plan on it soon to see if I can personally recommend it.

NixOS At the moment I personally use impermanent NixOS over ZFS, but the initial setup with 0 documentation for that was a nightmare. I wouldn't wish on my worse enemy to undertake something similar. But after that installing and setting up krdp was a couple lines in a config...

Final Comments Besides all that, my recommendation is just use something with KDE set up out of the box. Krdp has always just worked for both Nvidia and Amd on Xorg and Wayland. Fedora KDE is my recommendation based on personal experience as a beginner with next to no technical experience. But because of my experience bricking my setup trying to hack together rices, I would recommend Bazzite and Aurora because of the simple setup and rollback system if you want to tinker. Aaaand, use flatpak whenever an official package is available. You can install from Discover, aka KDE's app-store, with one click, you don't have to worry about package conflicts and it's currently the only supported option if you want to install windows programs through Bottles. Some loud people will disagree and say flatpak is bloat, but 100MB of extra storage being used for dependencies isn't that bad in this modern era of Terabyte SSDs when the reward is simple installs and more supported software options.

TLDR: Use distros with KDE as the default, and try Aurora or Bazzite for a decent out of the box experience.

edit: typos and formatting

Just install xrdp, do xrdp <url>, be done?

I don't know of a distro that does.

You can start remmina from the terminal, it should spit out an error. I believe, you need to install additional libraries for full rdp support, but it should tell you

Upgrade it to Ubuntu 25.10 ?

The session needs to be active! If the screen sleeps or is locked it wont connect. This will be fixed in Fedora 44 (soon to be released) but there is an extension that can be used as a quick fix in the meantime.

You patient enough to build a distro for yourself?

If so, Gentoo.

Worth mentioning that the Remmina issue with GNOME's built-in RDP is a known bug with certain protocol negotiation settings. Try these in Remmina:

1. Connection → Security → set to "RDP" (not "Negotiate")
2. Under Advanced, disable "Network Level Authentication"

If that doesn't work, xfreerdp from the command line is more reliable:

xfreerdp /v:your-server-ip /u:username /dynamic-resolution

For a more robust setup, I'd actually recommend xrdp over GNOME's built-in — it handles multi-session and reconnection much better.

Might be off topic but if you are thinking of rdp for 3D modelling or gaming then IMHO there are better solutions, e.g. https://moonlight-stream.org/ or https://selkies-project.github.io/selkies/ so I'd argue it's not a distro question, more a client/server one.

FWIW I moved away from Ubuntu to what it relies on, namely Debian, and for modelling (e.g. Blender) or gaming (Steam, 2D, 3D, VR) it's been great.