> The calendar then would track the Earth calendar as close as possible, with shortened months to accommodate for the longer days.
Why bother with months? Why not just count weeks? You could use something like the ISO 8601 week calendar – the year is divided into weeks. Weeks run Monday (1) to Sunday (7). Every year beings on a Monday – ISO 8601 has two years, the Gregorian year (starts on 1 January) and the ISO week year (always starts on Monday). The ISO week year always contains a whole number of weeks, either 52 or 53, so the first day of the ISO week year is often a few days before or after 1 January. 2023-W09-2 is an ISO week date, it is the 2nd day (Tuesday) of the 9th week of 2023.
So, here's my idea for a Martian calendar. The base unit is the Martian day (sol) of 24h39m35.244s. 7 Martian days is a Martian week. The calendar year is based on the Earth year, but it starts on the Monday of the Martian week closest to 1 Jan 00:00 UTC.