Mimo svátky budu mít volno i proto, že jsem si navíc vzal dopředu extra dovolenou, zatímco hodně mých kolegů si to nemohlo dovolit, ať už kvůli covidové krizi nebo zkrátka přečerpáním dovolené z dřívějška.

Except public holidays I will also have a free time because in addition I took an extra vacation in advance whereas many of my colleagues could not afford to take it either due to covid crisis or just (due to?) spending their vacation in earlier times.

“I will also have (some) free time in addition to the public holidays because I arranged extra leave beforehand / in advance, though many of my colleagues couldn't, either because of the Covid crisis or (just) because they had used up too much (of their) leave (earlier).”

1. “Except” doesn't make sense here. It would mean I will have some free time, but not on the public holidays.
2. I didn't take the leave beforehand, I arranged (to take) it, I booked it.
3. Dovolená z prace = leave, not vacation.
4. “Free time” is uncountable (as in Czech jedno volno, dvě volna ??).
5. Although it's not “wrong”, I would avoid “could not afford to”. It suggests “neměli na dovolenou dost peněz”. “Couldn't” is enough in the context – we don't need to repeat “take it”. Alternatively: hodně mých kolegů si to nemohlo dovolit – many of my colleagues didn''t have that option/choice/lu­xury.

A proč se tam nehodí kratší due to (using up their leave).. ? Přijde mi to s tím přehlednější než 2× psát because (of). Děkuji.

“Due to using up their leave” is understandable (but not natural) here. The abstract verbal noun “using up” without the agent (who used it up?) doesn't work well. It's an “orphan”. I feel that the agent/subject needs to be identified with the verb more clearly (they couldn't take more leave because they had used it up earlier). The version I suggested is the simplest and most idiomatic in everyday style.

These “orphan” abstract noun constructions (where we don't know who the agent is, who did the action) work well (in context) in Czech, but often don't work well in English. You can ask any translator, or compare the (native) English translation of a Czech book and see how these “orphan” abstract noun constructions usually need to be tied more closely to the agent, the “doer”, in English.