It means that when I make changes in the YaST control panel, then reboot, the changes are gone.
They should be permanently saved.
You may be on to something …
grep hosts /etc/nsswitch.conf
# Valid databases are: aliases, ethers, group, gshadow, hosts,
hosts: files mdns_minimal [NOTFOUND=return] dns
I am also noting that /etc/resolv.conf is not updating correctly.
It always contains:
nameserver 8.8.8.8
nameserver 1.1.1.1
It should be updating with DNS information received during boot and DHCP addressing. (I think?)
It won’t if you’ve manually edited to start with AFAIR.
I found the fix to this.
/etc/resolv.conf was a text file when it’s supposed to be a symlink to /run/netconfig/resol
v.conf
I don’t think that’s the culprit. I have the same line - must be default. YaST modifications work well and persist, I have just added 10.66.66.66 with a testname - survived the reboot. Deleted it manually, all well. In
/var/log/YaST2/y2log
I can check the ruby module is readily reading the information from /etc/hosts. I had a wrong umask entry there - has been read in as address - hostname, too. 
If you want to go deeper you may try a similar test. After adding it in YaST, check /etc/hosts. Has it been added at all? Was /etc/hosts.YaST2save created or modified?
If no, maybe you can find something suspicious in /var/log/YaST2/y2log?
If yes, probably something is overwriting it? Ah, nearly missed this one:
I’m sure you must find some hint in the log file. Here, I have lines like:
2023-03-28 22:12:35 <1> pluto.mydomain(11397) [Ruby] cfa/hosts.rb(add_entry):148 adding new entry for ip 10.66.66.66
Does /usr/share/YaST2/lib/cfa/hosts.rb exist? If YaST doesn’t find your manual entry , maybe somethings wrong with that module? I’m on Leap 15.4, so my findings are not 100% representative for you.
Simplest try maybe force reinstall of yast-network?