The bottom of page 3 has the FESTIVO schedule, which means both Sundays and HOLIDAYS.
The HZ at the bottom of the table though EXCLUDES some times on Christmas (Dec 25) as well as Jan 1, Easter and May 1st.
So effectively, there are only 3 buses on those holidays from Florence to Siena and it seems there are 3 buses, but once of those has a V1 at the top, which means it only runs on May 1st. The V2 at the top of the column on the other two buses excludes Christmas, Easter and Jan.1... so this in the end means there are no buses from Florence to Siena on December 25!!
I checked the timetable for the normal 131 bus (not fast), same thing applies. Same from Siena to Florence.
I also checked FLixbus, their bus that connects the city also doesn't run on Dec 25 (it does on the 24th and 26th).
If you have to get to Siena on the 25th, your only option is the train: check www.trenitalia.com for timetables between Florence and Siena, there are plenty, all take about 1.5 hours and about half require train change in Empoli.
As for heading to Rome, the train will also be the only way.... and those will have you change trains somewhere, whether in Florence, Grosseto or Chiusi. Check the site and search -- I cannot add links here because the search results are based on cookies on your computer, so the links expire and don't work after.
My suggestion is to avoid travel on Dec 25 and enjoy Florence! Or plan to travel to Rome the day before, spending Christmas day already there.