Tear in sidewall on puncture protection belt - does it need to be fixed?

The only action I would take is to carry a tire boot kit such as Park Tool TB-2, and inspect the area often after riding, takes only few seconds to inspect it once. If it remains static over time, you can stop the regular inspections. If you want to be thorough and spend 5 minutes you could obviously deflate the tire, remove it from the rim, and inspect the area not only from the outer side but also from inside. I suspect the bias ply cords of the tire remain undamaged.

Usually bad sidewall tears cause the inner tube to explode immediately, making a loud bang. In theory there could be a sidewall tear that gets progressively worse over time.

The only way a sidewall damage can be harmful is that the inner tube explodes, either immediately due to a big hole, or alternatively poking slightly out and being abraded slowly.

It's always a good idea to carry all supplies for repairing tire damage: patch kit, boot kit, pump, spare tube, tire levers, necessary tools for removing and replacing the wheel if not quick release wheel, etc. Not only because of the damage you already have, but also for potential future damage. If you ride in conditions that can create the minimal probably harmless damage your tire has, it's possible the next ride creates even greater damage, something that damages the inner tube.

And also remember that unlike inner tube patches that are permanent, tire boots are only temporary. A damaged tire needs to be replaced.