[daddylonglegs]

Well, the Martian solar day is a directly relevant measure for a mission that depends on charging batteries each day by solar power. I could see that being used for a lot of planning and operations.

UTC (and international atomic time - TAI) is an average measure of elapsed time that already needs adjusting for relativistic time dilation. None of the accurate clocks used for TAI are at sea level but TAI is reported as though you had all your caesium atoms ringing away at sea level [0].

Everyone else adjusts their clocks with reference to this, making allowance for propagation delays where needed. This includes things like navigation satellites (GPS, Galileo, Glonass, BeiDou etc) which have accurate clocks and significant (for their operation) relativistic dilation.

Since we already have to deal with relativity and propagation delay here on earth I suppose that, if your mission can still ping mission control here on Earth, then you can still set the system clock to UTC or TAI [1]. You will need a look up table for local sunrise times and the like but that seems quite simple compared to the mess that tzdata has to allow for back home.

[0] As I write this I realise that I don't know if TAI will be adjusted for sea level changes or not. Anyone know?

[1] Using TAI might save you from leap second problems while landing on an alien planet.