I am landing in Rome at 7:45 on the 15th of May and have a reservation for a train to Florence at 11:35 AM
jeanrose, you are flying into Rome and taking a Trenitalia (or Italo) high speed train to Florence.
As I wrote: It's the company running regional trains in Lombardy (and Tuscany) that's going on strike. Different trains, id not different companies.
The only thing I am still confused about is that another poster, Roberto, stated that "the strike is on the 15th and It ends at 2:30 AM on the 16th
Roberto is right and I was wrong about the times . The site says:
From 03:00 AM of May 15 to 02:00 AM May 16 Company: Trenord
From 03.31 AM of May 15 to 02.30 AM of May 16 Company: Trenitalia.
Ps I don't know where I copied "15:00" from on the Strikes site, but I am sure I copied and pasted it! The guaranteed time-slots I pasted are right: https://www.trenord.it/assistenza/informazioni-utili/in-caso-di-sciopero/