MDBT42 crashes with motor powered by its battery

The Vin pin of the MDBT42Q breakout goes to a regulator, and that regulator drops some voltage (don't want to look up right now, but probably couple hundred millivolts). If you use a battery (for example the CR2032) that's less than 3.6V, connect it to the 3.3 pin.

And not exactly what you asked, but a motor - I assume it's running not only for milliseconds - even at 10-20mA is huge for a CR2023.
You should try somewhat bigger battery. Watch out for it's voltage! If it's below 3.6V, connect to the 3.3 pin, if it's over that, connect to the Vin pin. For example, Li-ion, Li-poly must be connected to the Vin pin. LiFePo4, CR123A can be connected to the 3.3 pin.

Sat 2021.05.15

from post #1
re: 'By the way the MDBT42 stop crashing if I add two big capacitors'

While I don't have that hardware to test, It is likely that:

As a motor is inductive and requires an initial massive draw to get going, that after the caps charged, there was sufficient current to start the motor turning. A coin cell isn't designed for high current spikes. see spec p.1 'Standard Continuous Discharge Current 0.3 mA'

re: 'but the MDBT42 crashes'
As E = I x R as current draw goes up, voltage goes down. It is likely that battery voltage fell too low for the MDBT42Q to operate.

I agree with @AkosLukacs at around ~260mAhr a CR2032 coin cell wont last that long

https://www.duracell.com/wp-content/uploads/2016/03/CR2032JCS0820.pdf