You can test almost anything with Bats, assuming it accepts input and produces output or an exit code. Bats is commonly used to test scripts, but it can also be used to wrap characterization or integration tests or API "contract" tests around an executable (eg run my-thing.bin -h ; assert_exit_code == 0 or to run a series of commands and test the results across various parts of the system (eg docker ps | grep bats ; assert_line 'bats/bats:latest').
When testing a shell script with bats there are multiple ways to perform the tests. You can do a "blackbox" style run my-script.sh --some option --other-flag and assert certain outputs and status codes and check for the presence or absence of temporary files in /tmp (if it was supposed to create or clean them up), or the absence of oh-poop.log files if the script triggers logging when it hits an error. Or you can do individual function testing and examine the environment variables after executing individual functions to check for any state that you are tracking between functions (in global variables) or to ensure that local variables didn't leak outside of their scope.
Personally I prefer a combination of approaches in order to build up a script, then if my script is going to be called primarily as an executable and not sourced I keep in mind that if I want to do any major refactoring, most of my function tests will need to be touched, but my behavioral tests shouldn't need changed, and if they DO need changed, then I am altering my external/user facing API and I need to bump the script version according to the semver.org recommendations.
When using the script calling run style you should know that there are $status and $output variables used by Bats that you can also use to examine the output, but other than for debugging why your test assertions are failing you should turn off displaying these in order to maintain compatibility with other TAP compliant parsing tools (ie a TAP parser/reporting tool in your CI system). To make these visible in the test output you need to use echo '# sometextlike status:' $status >&3 or echo '# sometextlike output:' $output >&3 to get them to show up with the test results. This is due to how Bats manipulates the file descriptors to monitor STDOUT and STDERR for testing.
When sourcing a script and calling functions directly there is NOT an $output variable, but $status and any other environment variables that are in your sourced script are available, and if your function creates/sets a new variable it should be available after the function is called. If you source a script you can also run somefunction and in this case you will get the $output as well.