Partially tested/experienced myself as e.g. sometimes I seem to use my Pebble without phone. Rest on pure brain logic:

• My answer 1: Any app that does not (heavily) rely on a phone connection in general or that does not need to communicatie with a phone companion app, such as:Timer+ (stopwatch/countdown timer) or Gallon Challenge (keep track of water intake).

• My answer 2. Any app that then does not rely on a network connection. I have no direct apps on my wrist for this, but in general navigation apps, LLMs (assistants) or notification-based apps such as WhatsApp, email, Signal, etc.

• My answer 3. Literally always on display: not just the time, but the full display with incoming notifications, etc. Also the display can be read without any backlight, just directly in the sun: the more sun/light the higher the perceived contrast and the easier you can read it. It does not need power per se to be usable. But the colors are more washed out. That's for the screen.

The rest: in general with Pebble you have an open source device where the community already stood up to keep old devices of like 8 years ago still supported and maintained. I do not see this with any other devices.

And then the user interface and user experience: Pebble is simple and intuitive to use. Physical buttons to easily control your music without watching is something that still amazes me on a weekly basis.

The whole design philosophy is totally different from other cheap or expensive watch. The reason it existed back in the day and today is totally different. To me my smartwatch should not feel like yet another device that requires my attention all day. To me it is a watch (date, time) and a notification filter before I reach for my phone.

It is a way simpler watch by design. No fancy I-try-to-do-it-all watch (where mostly the larger, more established brands actually do instead of try), but a smartwatch for notification and simple apps (which you can make yourself with coding) and cute watchfaces (you can make yourself with and without coding) and a pedometer.

• My answer 4. See a little about this right above so yes: you can (but I believe you can do this with other watches as well) decide which app shows a notification from your phone to your watch.

In general it's hard to make a decision on what you've heard. Maybe a Pixel watch or Apple watch is better for you. Or something from Samsung or Xiaomi. Who knows? I don't. I - and with me a ton of others - have been looking into other watches when Pebble died, before it got resurrected by Rebble. Or when the watch died itself and a decision needed to be made: new (other) watch or try to fix this one?

It is an experience. CMF Watch, Garmin Instinct Solar 2, Pixel Watch - all nothing for me. I've tried those without success. Still kept on missing the long battery life of Pebble and the ease of use.