Any Old Port in a Storm - S3-E2
Question: As a homicide detective, why would Columbo have been present at an apparent drowning incident?
Answer: "Apparent" drowning answers your question - things are not always as they seem. Drowning could be accidental, but it could also be a murder in disguise. Moreover, the actual cause of death has not yet been determined - accident, suicide, murder, or natural cause (e.g, heart attack while swimming). Columbo would be there to investigate if anything looks unusual for it to be a mere drowning or if there is evidence or suspicion of something else.
This was just on TMZ.com's "Aaron Carter Dead at 34" (11/05/2022): "Law enforcement sources tell TMZ... homicide detectives have been dispatched to the scene but we have no information or evidence of foul play. It's standard operating procedure for homicide detectives to investigate such [drowning] death scenes."
Answer: In the show, he was already a Lieutenant. A promotion would put him in the next rank up, which for the L.A.P.D. would be Captain. However, some of a Captain's duties would be overseeing other officers and ensuring they're compliant with policies, regulations, and standards. It would also most likely take him out of the field. This is something Columbo has no desire for as he rarely goes to police HQ's. Nor does he show interest in compliance and standards (for example, not going to his semi-annual evaluation at the firing range). However, he could still be assigned to a higher pay grade based on expertise, which is a form of promotion that does not include rank advancement. This would be going from Lieutenant I to Lieutenant II. I don't believe in the show it's ever started what his pay grade is. Although, in s02e01 (I believe) he mentions making $11K a year. Whether or not this was a true statement on his part, if you could find pay scale information for an LAPD Lieutenant in the 70's, it could give you an idea of his pay grade.
Bishop73