Problems with the battery duration

Sorry - yes, Wake on button is best - I wrote the wrong thing.

Can a permanent notification triggen the high power mode without seeing the notifacion in the bangle?

No - it's just when data is sent to/from the Bangle.

How do I dump the logs? Where to find them?

https://gadgetbridge.org/internals/topics/logs/

but is very strange that after a factory reset I get like a week of low power usage.

What if you just factory reset and leave it not connected to a phone? What's the power usage then?