You can find the logs by running:
log show --predicate 'subsystem == "com.apple.xprotect"'
To persist them, you could just save it into a file, like this:
log show --predicate 'subsystem == "com.apple.xprotect"' > mylogs.txt
You can find XProtect's various security definitions in this folder:
/Library/Apple/System/Library/CoreServices/XProtect.bundle/Contents/Resources/
For example look at XProtect.plist
and XProtect.yara
. If you want to prove to yourself that these are actually updated by Apple - take a copy of them. Then compare that copy to your files a month or two later.
If you're still very suspicous that perhaps Apple is just claiming to scan for malware, while actually not doing so - even when that would include making fake documentation for it, fake software for it, fake definition files, and fake update processes for the same - you can just check that it does for yourself. Sounds like it would almost be more work for Apple to fake scanning for malware rather than actually doing it -- while at considerably risk of any system expert or programmer exposing them. Doesn't make sense, but if you really want - noone's stopping you.
Checking for yourself could include actions such as intentionally introducing a malware file (inactivated) to the system, and checking that the XProtect detects it. You could also do code analysis on the XProtect binaries to make sure that it does what Apple says it does.