KDE Connect has been mentioned before. You can supplement this and other tools by using a VPN so that both endpoints can see each other even if the underlying network does not allow this. My preferred solutions are Tailscale (managed, cloud-based) or Headscale (for self-hosting).
Yes, XMPP with proper TLS on the server side and Conversations or one of its forks (preferably fetched from F-Droid) using OMEMO encryption should be good enough. If you are brave or paranoid, give Tox a try: https://tox.chat/
Maybe the first question is what your budget is, both regarding money and time. For example, you could buy a pre-configured NAS from Synology or QNAP, which requires less technical skills but more money, or a home-made solution reusing used components (but fresh disks for reliability). Depending on your electricity costs, you may want to choose a low-power solution or something which you power off when not used. For storage, maybe a three-disk RAID5 is a good compromise. For backups, plain S3 cloud storage encrypted via restic is a good idea.
If at all, you want to use Gentoo’s ebuild system, which can be seen as some kind of superset of PKGBUILDs. I guess one could write a Python script that “dumbs down” ebuild scripts to PKGBUILDs for simple packages (excluding complex stuff like kernel, KDE, …). The main challenge, as pointed to before, would be maintaining a table mapping package names between distributions in order to get the dependencies right.
The “C” in the progress bar is alternating between “c” and “C” to give the impression of munching.
There is some information missing in the problem description. For example, if you close the lid, does the computer suspend/sleep/hibernate? It may be that when the computer sleeps something “breaks” or it may be that the act of physically closing/opening the lid has an effect (e.g. because the WiFi antenna is embedded in the display frame).
Some time ago I had a similar problem with Tailscale and sleeping. When Tailscale initializes itself (at boot), it has to interact with another service to communicate which DNS servers have become available (e.g. 100.100.100.100). Several implementations of such services exist (resolvconf, openresolv), in my case systemd-resolved. During normal operation, resolvectl status (if using systemd-resolved) shows which DNS servers and which search domains are configured for each network interface such as tailscale0. Now, there is a bug (or feature) that systemd-resolved “forgets” the DNS configuration it got from Tailscale when the computer is put to sleep. So, when the computer wakes up, name resolution via Tailscale no longer works, giving you the impression that Tailscale itself is not working, although Tailscale’s low-level functions are still operational.
My “solution” was to write a small script that gets executed when the computer wakes up which sets again DNS server and search domain for network device tailscale0.
ArchLinux’s pacman with ILoveCandy option enabled.
My setup is smaller, but when my venerable old router died about a year ago, I acquired an Asus TUF-AX3000_V2 where I installed FreshTomato. One can login via SSH and dump all settings for backup. Likewise, individual or all settings can be done on the command line instead of the GUI. I have a script on my computer that reads CSV files with MAC addresses and more to apply changes in an automated way.