OK, I bought a lightly used Crucial P1 M2 1TB drive for cheap + Orico M2PV-C3 USB-C 10Gbps enclosure (it's a quality cheap enclosure and really provides up to 10Gbps speed, so I can recommend it for those who can't afford Thunderbolt/USB-4 drives). Successfully made a bootable Monterey 12.5 USB drive with standard Apple Disk Utility, only to find out that system gives me the infamous "SDErrorDomain error 108" message when I actually try to boot the Mac from it.
Then I just used Carbon Copy Cloner and cloned my internal drive to the USB drive, it went smooth to my surprise and provided me with bootable drive without any problems. It works well and quick (even though boot now takes about 25s instead of 10 or so). Just don't use Samsung drives, I read they have problems with TRIM on MacOS and boot in more than a minute.
But now I have a big question. How do I update MacOS on this external drive when new update comes, just like it was an internal drive or there are going to be some problems?