Hello Sandra,
I'm not sure to follow you, as far as I can tell, your screenshot does not show a FP from the SonarJava rule itself, but the error message provided by eclipse IDE on a code which does not compile (of course due to "test" being not effectively final).

I guess you ended up with this code after modifying the code, but it would have been maybe easier if you would have provided the code generating the SonarJava issue, prior to the modification. I guess it's something similar to this:
In such case, the issue message is indeed not relevant and using a Supplier won't be possible.
Now, the essence of the rule is to not evaluate logging arguments, in order to not needlessly impact performance. As suggested in the compliant solutions from rule descriptions, another approach is to check log level before actually logging:
if(LOGGER.isLoggable(Level.FINE)) {
LOGGER.fine("test = " + test);
}This code won't raise an issue of S2629.
Anyway, I created the following ticket to reword issue messages in such case:
SONARJAVA-2380
Cheers,
Michael