I understand that there are sea level-optimised and vacuum-optimised nozzles, but why optimise for sea level when the rocket doesn't spend much time there? I would expect the first stage nozzles to be optimised for maximum specific impulse over the mission profile. Is "sea level nozzle" a misnomer, or is there only a slight difference between my expectation and a true "sea level nozzle", or is there a real need to get a bit better specific impulse for the first minute or so?
It's not quite a misnomer. Sea level nozzles aren't optimized for sea level, they are designed to be operable at sea level. You can see the "sea level" Raptor for instance produce Mach diamonds due to the overexpanded exhaust being compressed by the surrounding atmosphere. These go away as the vehicle approaches the altitude the nozzle was optimized for.
A vacuum-optimized nozzle with no altitude-compensating features wouldn't just produce slightly overexpanded exhaust, it would experience flow separation. This could cause control issues, vibrations, or directly damage the nozzle, so engines with such nozzles generally can not be operated at sea level.