Is it reasonable to expect some sort of 'bloom', or other 'after-image' effect when in the vicinity of said weapons fire?
PC's were within 10m of an assassination, and rapidly figured out the weapon type with no visual clues.
They may not have "seen" the laser shot ... but at less than 10m away they would have HEARD the damaging effects of the laser shot.
Even if the laser sniped from a long way away (so there's no "trigger pull" noise for them to hear) ... on the receiving end if that laser damaged flesh there would be a distinctive vaporization/cauterization "steam explosion" where water laden flesh is
very suddenly raised in temperature past the supersaturation point and violently explodes as the water in the flesh transitions from solid/liquid into being gas/plasma due to thermal shock.
In other words, lasers would inflict characteristic wounding effects that would be readily recognizable as being caused by a laser.
If the PCs were in an enclosed room and no windows were broken by a bullet, that would be another clue that a laser was used.
So being able to make that determination with no visual clues is possible, and also a likely assumption given the right audio clues at that proximity. Those audio clues won't necessarily "work like a tracer" to point back at the shooter (so low signature upon firing still makes sense), but an experienced infantryman/security type would very quickly recognize a wounding effect dealt by a laser weapon.
I've always assumed that laser rifle/carbine/pistol beams are either IR/UV light, and therefore invisible to the human, and some sophont eyes.
Up through TL=12 in CT, lasers can be anything in the IR, optical or UV spectrum ranges.
At TL=13, laser rifles/carbines/pistols are made as X-ray lasers, which is why they get a deadliness/damage bump at TL=13+ in CT.