Issue with delayed inverval interruption having a timer Crystal installed

Perhaps a MDBT42Q could be an alternative

Yes - it can self calibrate the RTC based on the high speed oscillator, but it's still not entirely accurate.

I'll then use a Pico without the Crystal and a DS3231 module as an external reference.

That's probably the best bet for a standalone clock. Even external crystals like ABS06-107 are 20ppm accuracy (so not much better than just using the high speed oscillator) , but the DS3231 is 2ppm - so 10x more accurate!