Note that we already have a PageTest at https://github.com/xwiki/xwiki-platform/blob/848287c4ab19b06af87280c3fe0d18004fd773a2/xwiki-platform-core/xwiki-platform-logging/xwiki-platform-logging-ui/src/test/java/org/xwiki/logging/LoggingAdminPageTest.java#L74 that is covering set-level, unset-level, and the unknown-logger error path at the rendering level (mocked LoggerManager).
There's also https://github.com/xwiki/xwiki-platform/blob/53ce83181a6e2ec2a97587190c1b6948c1bc6b6c/xwiki-platform-core/xwiki-platform-logging/xwiki-platform-logging-script/src/test/java/org/xwiki/logging/script/LoggingScriptServiceTest.java that unit-tests the logging script service + PROGRAM-right check.
What we are strictly missing:
Now if we implement the missing checks, then the page test becomes almost irrelevant (except for the unknown logger part)...