Absolutely doable. I have had an Ubuntu on a 16Gb stick for years that used any time I had to log into my gmail from a borrowed/friend/relative computer.
I can’t name specific solutions off the top of my head as I haven’t done it in a while, but Yes. There are many live distros that offer an optional ‘overlayFS’ (I think that’s the right term) which reserves some of your portable drive’s storage for persistent changes to apply over the base live FS.
Combine that with git and/or NextCloud or an SSH file mount or three and you could probably come up with a complete mobile setup that also has quick access to whatever home server infrastructure you need. 128GB or 256GB USB sticks are pretty cheap now which is plenty for a spacious install. Or even a small USB SSD.
Don't use USB stick, it has really awful random read / write performance. I recommend fast SSD with cache. I tried USB stick solution several years ago and it was so laggy it was unusable
I inherited a crappy laptop (4 core atom processor, with 4 gigs of RAM, fear the power!) because Windows was running slow on it. I decided to try different Linux distros booting from a USB and had no issues. I literally ran the system for months off of a Sandisk USB drive, and it was faster than the spindle drive in the machine.
My recommendation is, don't cheap out on the USB drive. No-name drives are fine for word files, but the performance increase from a Sandisk, Samsung, Kingston or equivalent is worth it for any media transfers and will work fine for a bootable Linux.
A good workaround for this is to add toram to your kernel command line. This loads the whole image into RAM before booting, which speeds things up dramatically at the expense of using more of your RAM while idle.
I think you can simply install a Linux distro on a USB drive. You should use something fast like a USB-C hard drive and you’ll have to think about where to put the boot loader. But if you’re careful, what you have in mind should work.
You can use ubuntu, debian, or a few other live distros with "persistence" which is relatively easy to configure. This is neat because live versions usually come with cool features like auto configuration of devices and displays. You can even create a persistence boot of live isos on ventoy, which is honestly what I'd recommend.
I've been using PopOS and Steam installed in Flatpak, as well as native and both have worked really well. Lutris i have installed through flatpak, as otherwise it sometimes gave me issues. This is running really well on my AMD 5950x and 6800XT
The way it was explained to me was Fedora = RHEL Alpha, CentOS Stream = RHEL Beta, RHEL is Stable, then there are downstreams who build against RHEL. Only those who are downstream of REHL are effected by the changes. Both Fedora and Cent are necessary development platforms to support everything that eventually makes it down to RHEL in stable condition. They both depend on RHEL for funding, but RHEL depends on them for testing.
Debian Stable + Backports, with a few customized flatpaks. I don’t care that my desktop apps are not bleeding edge. My system always works, and games run great.
I'm using Nobara. It's a gaming tweaked Fedora with a bunch of gaming and steaming related software preinstalled and configured. Works well in my experience.
Same, started using it on a pc connected to my tv (for a console like experience, boots straight into gamescope/steam).
Now I also use it on my desktop (replacing Ubuntu).
Mint for my desktop, SteamOS on Deck. Both do what I need, and the only issues I've run into since switching have been random things like GOG not having an updated Planescape Torment build that works out of the box. I don't play many online competitive games with like invasive anti-cheat stuff, so I haven't run into a ton of compatibility issues.
It is doable to install an OS onto a flash drive or external drive, but from my experience it was really slow. Just need to make sure to then boot the machine to the USB device. Some machines you might find it difficult to change that in the BIOS.
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