When using a loaded crossbow (the bug occurs with arrows and fireworks rockets) you can attempt to extinguish the fire by punching.
The expected result is the fire extinguishing, but it fails to do so with loaded crossbows.
It happens in survival and creative mode. I have seen this bug on Windows 10 and Xbox Series X. I have seen it on individual worlds are realms.
This issue is being tracked at MCPE-119568.