From 2035 it's going to be less accurate in exactly the same way. I'd argue bombcar's method is more robust.

I don't know of anything that actually requires UTC to be within 1 second of average rotation-based time; having it within 2 or 3 seconds is extremely unlikely to actually break anything. But we do generally want to have measured time roughly in line with Earth time in the medium to long term.

Today it is within I think +-3 hours of earth time (China being the worst offender), because of timezones and DST. If it ever gets worse than half an hour in a country, they can always change the timezone... or just, like, change businesses' opening hours and stuff.

We have summer and winter time because that turns out to be easier than changing business hours. But I was just talking about UTC really.

How about clocks on Mars? Should these have Earth leap seconds? Time synchronization is already hard enough, complicating it with adjustments based on uneven planetary body movements doesn’t make much sense in a long term.

In the longer term Mars should probably have its own time scale. When we get to further colonization maybe we can use TAI for interplanetary use (but time dilation due to relativity effects is going to be a problem when going to other stars) while still using UTC on Earth.