If you take the suggested route via Luzern you will not be affected by track closures on your travel date. That issue is on two of the other routes between Switzerland and Milan.
The Bernina Express gets lots of love on this forum, and from the Man in Seat 61, but it works best for people who are heading to Varenna on Lake Como, and have more days to travel than you do. To reach it, you must travel far to the east, to Chur, then at the end of the train journey over the Bernina Pass, you travel back west from Tirano to Varenna. And right now there is a bus link in place between Tirano and Colico, where you meet the train to Varenna. That is scheduled to last through Sept. 8, land would mean yet another transfer, with luggage, between transport systems.
You can see the various routes on this map of the Swiss train system, with the scenic routes highlighted.
https://www.travelswitzerland.com/en/download/swiss-travel-system-map-en-2023/?wpdmdl=14294&masterkey=63a023c8da36c
I suggest you look at the very scenic Gotthard Panorama Express from Luzern to Lugano instead of the Bernina Express. This is a journey by lake boat down the length of the Vierwaldstättersee (aka Lake Luzern) to Flüelen, where you meet a train for the rest of the journey, over the pass, to Lugano.
https://www.gotthard-panorama-express.ch/en/
I find the route over the Gotthard Pass even more scenic than the Bernina route, and this option adds the very attractive boat trip. We did this last September with our son’s family, using the regional train instead of the named Panorama Express. Everyone loved both the boat ride and the train, with snowy peaks, hanging glaciers, and lots of waterfalls even in late September.
While we took the less pricy regional train for this, I am recommending the actual Gotthard Panorama Express to you in part because they offer checked luggage service for the transfer between boat and train. You check your bags at the dock in Luzern and pick them up in Lugano, where all you need is a taxi to your hotel for the night.
https://www.gotthard-panorama-express.ch/en/stories/luggage-service
So—-one night in Luzern, in a hotel with view of the river if you like, then the boat plus train right to Lugano, for your second night in Switzerland. The next day take the train the short ride from Lugano to Milano Centrale, where you take either a Trenitalia or an Italo train directly to Florence. Italo is a private company and they offer senior rates as well as other discounts. Their website is very user-friendly. Trenitalia has senior rates only if you join their Carta Freccia program, but they do have other discounts possible. Some have reported difficulty with Trenitalia, particularly with certain US credit cards. Also you must use the Italian names for all the stations, so look for Firenze S.M.N. For your Florence destination.
https://www.italotreno.com/en
https://www.trenitalia.com/en.html
Total number of transfers between trains with luggage: one at Basel SBB, and one at Milano Centrale. From Luzern to Lugano you can use the checked luggage service if you take the Gotthard Panorama Express; otherwise you will have one more transfer between Luzern and Milan.