So, does this means the speakers can handle the pink noise the processor/receiver generates as part of the room calibration without worrying the drivers will be damaged (especially the tweeter)?
This is one of the reasons I never run the calibration process after replacing my old speakers with GE set.
I know the pink noise is generated at 0db (reference level) which is very loud.

Why are you concerned about this damaging the tweeters? I cannot find any information indicating damage to any speaker from pink noise calibration, nor that ribbon tweeters are susceptible to damage.

That said, I’d follow goldenear’s break-in and setup guides, which advocate for eq off.

How loud is loud? How big is the room? How loud do you want to listen? How much power can your amp deliver before clipping? There's lots that impact how loud you can make speakers without damaging them. The Triton One's can play loud enough in most residential situations to satisfy just about anyone. But if the listener wants to play the latest Mad Max flick (for example) at ear splitting levels it's always possible to damage any speaker. Used responsibly, in a typical room there should be no issues using a One.

I think your amp is more important here. My T1s will deafen me before they’re damaged. Not being loud enough is not really a concern one should have. I’m powering them with an Emotiva XPA-7.