They are required to "self-quarantine" for 14 days, but it is not strictly enforced at the border. More like random checks.
I didn't go to Florida, but did a similar trip. Superchargers are considered "essential services" like gas stations.
There is a possibility, if the host of the supercharger (ex. a mall) is closed, the access may be blocked. I encountered only one such restricted garage and it was open and free for supercharging. All the others were gas stations, hotels, strip malls.
There was a thread about this and it only got 1-3 SC stations listed, all out west.
In most of the country, there are enough superchargers that you aren't in danger of getting stranded. If there is a section with only 1 supercharger, probably they won't allow it to be restricted.