Don’t you mean from 1 to 11? (And 3 is not a valid option.) Sorry, I saw an opening for a stupid joke and had to jump.

The results have made me realize that the bash way of doing this is just not worth attempting, and a Python script is much more simple. At the end of the day, I ended up using this GIST with a custom handler function:

https://gist.github.com/dperelman/c1d3c966d397ff884abb8b3baf7990db

class MouseProfile(Enum):
    DEFAULT = 0
    BLOONS = 1
    GAMING_COMMON = 2
    CALL_OF_DUTY = 3
    REALM_GRINDER = 4

def handle_change(new_state: dict):
    """
    Using `libratbag`, switch the profile of the mouse based on the active window title.
    """
    # Get the title of the active window
    title: str = new_state['title']
    profile: MouseProfile = MouseProfile.DEFAULT
    match title:
        case "BloonsTD6":
            profile = MouseProfile.BLOONS
        case "Realm Grinder":
            profile = MouseProfile.REALM_GRINDER
        case _:
            if title:
              if search(r"^Call of Duty.*", title):
                  profile = MouseProfile.CALL_OF_DUTY
              elif search(r"^Deep Rock Galactic.*", title):
                  profile = MouseProfile.GAMING_COMMON
    # Send the ratbag command to switch the profile
    run(["ratbagctl", "Logitech", "profile", "active", "set", str(profile.value)], stdout=PIPE, stderr=PIPE)