Powering the blue pill board from laptop and using another power supply at the same time, will this cause problems?
This works fine on the Arduino using a CNC shield from USB 5V with 12V power or laptop charger 19.5V with good common grounds.
However if the signals are on long cable, you may experience errors on Data if the charger is connected from Charger Common mode noise.
If you sequence power while connected the unpowered digital interface may have problems if un protected , so a series R of 10k will protect it but may reduce noise immunity and high speed limit.  USB is safe but perhaps not unknown logic interface.
But from your comment an old PC PSU that has all the 12V power and logic level supplies should suffice with no other supply needed.