If you use passwords of a small enough size that this would really be a problem (like four digit PINs or your "aaaaA1!" example) then your password isn't delivering adequate security against brute force and so you've definitely lost.
If you use passwords that are big enough to make brute force impractical anyway then this "feature" will never make any real difference and is just a waste of time at best, and since it adds complexity it's another place to hide bugs.
Having a PwnedPasswords check (not this silly "repeating characters" test) makes sense if you allow users to enter passwords. Whereas if you generate passwords of decent length and at random then they're random so there's no purpose in checking them.
If you use passwords of a small enough size that this would really be a problem (like four digit PINs or your "aaaaA1!" example) then your password isn't delivering adequate security against brute force and so you've definitely lost.
If you use passwords that are big enough to make brute force impractical anyway then this "feature" will never make any real difference and is just a waste of time at best, and since it adds complexity it's another place to hide bugs.
Having a PwnedPasswords check (not this silly "repeating characters" test) makes sense if you allow users to enter passwords. Whereas if you generate passwords of decent length and at random then they're random so there's no purpose in checking them.