Clean up Logging page top bar (#6281)
Fixes https://github.com/flutter/devtools/issues/4921
https://github.com/flutter/devtools/assets/1386322/ebe4f959-72b3-4d02-a755-a1bbef7fb577
# Open question
The structured errors are saved in the service, not in the local preferences. Should we have a way to somehow let the user know that this setting is saved in their app?
