It runs basically the same PebbleOS, so they'll work with any app that works with the original Pebbles. They plan to keep using the community app hosting at https://apps.rebble.io/. There's also GadgetBridge that's compatible. Eric mentioned on HN the intention for an official open source library that can be used to make other companion apps too.

The hand-wavy answer is: go check the code and find out, however that's not accessible to everyone.

The helpful answer is: The code is out there, and the launch date is far enough away that those who do understand it enough to make that distinction should have the time to do so before it ships, so time will tell.

The Rebble folks probably are the closest to knowing, given they've been hacking on the current app for the past several years.

My guess is probably not. The target audience probably wouldn't be cool with it.

Also, there are 3rd party watchfaces and apps that will be available, so that code will need to be evaluated too. So, it's more complicated than a single yes or no.

One thing about the Pebble - and, I assume, these watches - is that they didn't have WiFi or LTE, only Bluetooth. So it wasn't possible for them to do any communication except through the apps already running on your phone. So, broadly, it's a no.

Your response says, "not epaper" which is categorically wrong. I assume you meant to say "eink"

Where exactly is that quote from? I had a look through the product page(s) and could only find e-paper being mentioned...

I believe these are sharp’s memory in pixel lcds. They’re much lower power than something like the game boy screen as each pixel retains its state and doesn’t need to be refreshed from the controller constantly. I actually like these little screens quite a lot. Worse pixel density and don’t look as good as e-ink when static, but still really Low power and can refresh way faster and smoother when needed.

Yet they are also the same - E Ink is an e-paper display.
Electronic paper is a category for any low energy display tech that looks kinda like paper, E Ink is a brand name for a "Microencapsulated electrophoretic display" from E Ink Corporation. Also just known as E-ink because IIRC they have the patent on it so nobody else can actually make them.