Time sync issues bangle js 2 (ios)

In general the Bangle may lose/gain 2 seconds a day of time when not connected to anything, but it shouldn't be much more than that - it's pretty standard unfortunately as most oscillators used for microcontrollers are only 20ppm (parts per million) accurate.

If you connect with the app loader then that can update the time for you (there is a setting, as usually doesn't mess with the time unless it's obviously not set at all).

I didn't even get new time when pairing it to my iPhone.

No... however firmware 2v19 does actually provide the functionality (https://www.espruino.com/Reference#l_NRF_CTS) it's just not handled in the JavaScript on the watch yet as it's pretty recent.

So if you're staying connected to the iPhone then it should be trivial.