It'd be nice to have a super-slim "upgrade the binary" mode that doesn't touch it if it's up-to-date, preforming only the GitHub API call to get the latest release.
I think the lightest-weight way to do this would be to require the invoker to provide the value to compare against; something like:
ubi -p beeper/bridge-manager -i "$XDG_BIN_HOME" --rename-exe "bbctl" --update-unless-at "$version" --verbose
... basically just the inverse of --tag; instead of "install this version", it's "install if latest is not this version."