Is this by design?
what kind of app? if it is a real app and is installed to one of the app folders it should show up. However command line tools will not
Don't think these managers install in Applications. So all installed by them are then qualified as cli tools I guess.
I don't think so. brew cask etc. does install standard apps fine
Do you have an example app?
Mole is for example an widely used app/tool 
to uninstall apps/analyse/cleanup etc.
ah ok, you probably mean the mole-cli. The mole mac app would show https://mole.fit
I think including CLI tools would be overkill - macOS alone has ~1500 CLI tools with a standard install. If you need some of them I'd recommend to add them manually to the launcher.
ok, I can also fzf them ofcourse, it was just a question.
if you want them to be listed, it would be simple to have a script in BTT that can retrieve them and show them in the launcher. I think brew by default puts them into /opt/homebrew/Cellar/
However for CLI tools "just launching" them is often not possible, having proper defaults for every item is probably not feasible.