What is the proper way to test a Bash function’s return value?

If it was the exit code and not the result, you could just use

if func arg; then ...

If you cannot make the function return a proper exit code (with return N), and you have to use string results, use Alex Gitelman’s answer.

$ help if:

if: if COMMANDS; then COMMANDS; [ elif COMMANDS; then COMMANDS; ]… [ else COMMANDS; ] fi

Execute commands based on conditional.

The if COMMANDS list is executed. If its exit status is zero, then the
then COMMANDS list is executed. Otherwise, each elif COMMANDS list is
executed in turn, and if its exit status is zero, the corresponding
then COMMANDS list is executed and the if command completes. Otherwise,
the else COMMANDS list is executed, if present. The exit status of the
entire construct is the exit status of the last command executed, or zero
if no condition tested true.

Exit Status:
Returns the status of the last command executed.