s approximately 668.591 local days long so there would be a lot of leap years, but this does not really matter.
For artificial space stations, adopting the calendar of the planet being orbited makes sense. For everyday usage (around say Jupiter), using the Earth calendar internally would be convenient (especially given the days are so short).
So, in conclusion there are some choices about what is convenient for humans to adopt as a convention in new places to live. A generic model can be parameterised to take into account these variants. The only fundamental concepts for a calendar are the longer period (for example the year), and the shorter period (the day). The most basic, but complete calendar is then Year+Day. Other formats to include months and weeks can then be accommodated on top of this, again with automated conversion between formats.
Include time of day
When the length of a day varies between planets converting date/times between the two planets means that the time of day will change. For example 10:00 on Earth (assume UTC) would be some other time on Mars, assume conveniently it is also 10:00 there. A meeting is held (ignore light delay inconvenience). We want to have another meeting the following week. On Earth that time will again be 10:00 (assuming Earth time is 'dominant'), but as a Martian day is 0.65979 hours longer we need to subtract that from the meeting time, so 7 x 0.65979 x (24 / 24.65979) = 4.494958. The Martian time for the meeting would be approximately 05:30 in the morning. Similarly, if the Martian time were 'dominant' then the earth time would be later in the day. When scheduling monthly, this would push the meeting into the 'previous' day on Mars. So, it is inaccurate to model just the calendar, the relative length of a day must also be taken into account. There are other confounding factors. Such as timezones, daylight savings and the relative light delay between planets. For this reason, it makes sense to reduce the number of variables. We can do nothing about relative light delay. However, we can do something about timezones and daylight savings, namely simply don't have them. Use a single meridian (on Earth UTC) as the single time for everywhere. This would mean that night and day start are at different times of the day in different places on Earth. So the local night would be from 06:33 to 18:33 (not exact) if you live in Fiji for example. You will get used to it. The first settlement on another planet would establish the 'base' meridian.
Yet another issue is the year relative to day/night cycles and the year relative to the 'fixed' stars. They are not the same, though conveniently on Earth there is only about 20.34167 minutes difference see
Adopting a Sidereal year as a standard would be more universal than a Solar year, and with the adoption of a standard meridian, this would mean the day night start cycles would vary everywhere. Again, this would be strange at first, but our descendants will adapt and for a multi-planet species that will be simpler. We would have to use a calendar conversion app to work out data/times and their conversion, but we cannot be a multi-planet species without technology, so that will simply be taken for granted by our descendants.
N body problems and Ellipses
All orbits are ellipses. All orbits are around a common centre of gravity. Any solar system is essentially an N body problem and closed form solutions do not exists, just numerical solutions
Elliptical orbits will also make the duration of seasons vary in length over time and the N body dynamics, especial in systems with multiple heavy bodies, such as multiple stars, will make calendars inaccurate after a time.
So the modelling above inherently has a chaotic element. This cannot be avoided, however humans will probably choose to live in relative stable solar systems for the most part.
There are also 'wandering' planets, bodies that do not orbit a star. These bodies will still have a day relative to the 'fixed' stars but no astronomical year. A 'year of convenience' might be appropriate here, choose a