How bad is a tiny avulsion fracture at the base of the proximal phalanx laterally 1x2 mm .?

It is not bad if : Treated well. The most important part of the treatment in my opinion is body tapping of the two fingers.

Which side?: If on the palm side of the finger, it is a volar plate avulsion. These are treated like sprains with early motion - just need to avoid hyper extension. If on the top side, it may represent a tendon rupture - these require splinting and sometimes surgery.