If you set the verbosity to "Info" in the Error/Debug Log, messages logged at level INFO will still not show up. Applying the following patch makes this easy to reproduce:

diff --git a/picard/ui/logview.py b/picard/ui/logview.py
index 9cb3ada5..c358c355 100644
--- a/picard/ui/logview.py
+++ b/picard/ui/logview.py
@@ -290,6 +290,9 @@ class LogView(LogViewCommon):
             QtCore.QObject.tagger.debug(level == logging.DEBUG)
             self.verbosity = level
             self.display(clear=True)
+            log.info("info")
+            log.error("error")
+            log.warning("warning")
 
If you now play around with the verbosity, the info message will only show up at verbosity Debug