Your grass should not have died over the winter. My St Augustine
survived a low of 9 degrees F and several continuous days with temps in
the mid 20s. So something isn't right in your care regimen. Chances are you are watering incorrectly and mowing too low. St Augustine should be mowed at the mower's highest setting. And even then you can skip a week or two between mowings. Mowing like this allows the St Aug to provide the most shade to the underlying soil and help stop crabgrass growth and seed germination. Tall grass also develops deep roots which need less irrigation.

Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.

Glyphosate is not the right product for that, use a SELECTIVE herbicide

Is there a selective herbicide that kills crabgrass but not St. Augustine?

You might try something with atrazine. Atrazine seems to kill everything except St Aug and centipede. It takes several weeks to see the dead plants, but it does work.

I like sulfentrazone on my Bermuda, but I have heard st. Aug is more sensitive to it. Atrazine gets good praise, but I've never used it

My understanding is that atrazine is only used on St Augustine and centipede because it kills all the other lawn grasses as well as broadleaf weeds.