Locked Outside Of My Rental, Likely For 3+ Days (florida)

I'm currently renting a house in SW Florida and the entrance door is equipped with a digital lock. Yesterday afternoon, I left the house with no incident. However, I came back at 5:20pm unable to get the door to open despite using the right code on the lock screen each time with no mistake. I tried for about 5-10 min and consistently got the odd numbers in a X pattern displayed on the screen as well as an unusual unlocking mechanical sound, which seems to indicate the digital lock is jammed and the solution could be to get the gears reset.

I tried a few things with the door and handle to no avail. Checking around the house, I was unable to find a way to enter as all windows and sliding back doors are locked.

The house is rented via a real estate company who has no emergency call service so I reached out to the Resident Maintenance Team by phone, and online by opening a maintenance/repair request ticket. It took 2 hours and two phone calls to get someone to actually handle the problem and all they did was open an 'emergency' ticket for me, which I had already done on my own.

Fast forward today, I haven't received any help and still wouldn't be able to enter the premises. About an hour ago, I received a ticket response claiming a contracted technician should be at the house some time during the day on June 3rd, which is 3 days from now, 4 if you include yesterday.

My questions are:

1- Is this situation legally considered an emergency despite it not being mentioned in the list of issues the real estate company's online portal acknowledges as emergencies?

2- Should I decide to get a locksmith to come today instead of waiting June 3rd, and seeing as the company, known for being greedy, unresponsive and incompetent, would most certainly refuse to refund the charge, how likely would I be to win in small court claims?

3- How likely am I to obtain prorated rent compensation for this in court?

4- A 4 day time response is not what I'd call an adequate emergency time response. My lease agreement being standard as far as I can tell, does being locked out of the house for that long constitute a lease agreement breach justifying termination on my end?