Thank you for all the detail, and reporting back about what you're trying! This is going to be long because that's just how I am, and I apologize in advance for the wall of text.
Let me summarize your system so we can think about it and what's going on.
Solar power:
12 250w panels is maximum 3kW energy when in direct sun.
5kW MPPT charge controller in the all-in-one inverter
8A maximum current on the string and wiring going to the inverter
No fuse or disconnect - so the only safe way to work on this is at night. (consider adding a disconnect and 10A fuse in the future)
Don't know what size wire is being used, or distance to the array. If it's thin wire (14awg, 16awg, etc) and/or long distance you'll lose some power, but since it's a high voltage array the loss won't be significant.
On a long sunny day you can expect them to generate 10kWH to 24kWH of energy, depending on a variety of factors. Foliage, overcast, rain, dust/debris will all reduce power output.
Inverter/MPPT charge controller:
5kVA inverting capacity
This is pretty much the same as growatt and several other "value" inverters. They have their quircks, but mostly work pretty well. The one thing that I've discovered is that the MPPT controller is very sensitive, and prone to failure. If your installer wired up all 14 panels to test on a sunny day, the MPPT controller is fried. The symptom of a fried Growatt/etc all in one MPPT inverter is that the solar panel voltage will equal the battery voltage. So during the day check the solar panel voltage using the inverter's interface and verify that the panels are about 370V.
Battery:
8 UP-GV600-6RE.pdf cells
424AH at C10 (ie, 42A) draw
Trickle/float charge voltage: 6.9VDC/cell, 55.2VDC pack
Bulk charge: 7.4VDC/cell, 59.2VDC pack
Nominal voltage: 50.4VDC pack
The pack will hold less than 21kWH
Gel batteries have good deep discharge characteristics, however they will last longer if only discharged to 50% depth of discharge. This is about 48.72VDC, and means you'll only be using about 10kWH of the pack's capacity - assuming it's in good condition. If it's already damaged then you might be able to count on 5kWH to 8kWH of usable capacity to avoid further deep discharge degradation.
Damage will occur under 48.72VDC, but it won't be really hurt unless it drops under 46.5vdc
Your battery cutoff voltage was 43V, and since you don't have grid power the "back to grid" voltage does nothing for you. So you have been drawing the batteries down into the danger zone, and they have been damaged. Gel batteries, however, are very resilient, so unless you've been doing this cycle for months you probably still have a significant amount of capacity left.
Load:
Daytime ??? over 8 hours
Night 200W over 16 hours
I understand you're calculating the time it's actually dark, but the panels won't generate much power until the sun is within 45 degrees off perpendicular from the panel, and you're not going to get much more than 8 hours of that. This is all very ballpark, though, every installation is different and without solar survey data I can only guess.
Note also that while you may only be consuming 200W overnight, the inverter could be consuming as much as 65W as well. Lastly, the inverter is not 100% efficient, nor are the batteries, and the wiring also has some losses. All together you're only going to be able to use about 80%-90% of the actual solar energy that the panels generated during the day.
Two things you can quantify here to help diagnose the issue is to find out how much power you're actually generating, and how much you're actually storing. Getting two power meters with AH measurements will help you with this. The solar array is high voltage, so you'll need a 500VDC meter, such as this one
https://www.amazon.com/Wireless-Charging-Capacity-Detector-Coulometer/dp/B0948NTML1 , for the solar power side, and you can get a cheaper one, such as one of these
https://www.amazon.com/Charge-Discharge-DROK-Voltmeter-Watt-Hour-Multimeter/dp/B07YWVCBRN for the battery side. I chose these because while they require you to disconnect cabling to put the cable through the sensor, and you still have to wire + and -, you don't have to come up with another cable and connection to connect a shunt. This type isn't as accurate as a shunt type, but you're not doing laboratory measurements, you just need a general idea of how much power you're generating and storing. While I've linked to the amazon listings, these are the cheap generic models you'll find from many places, so you should be able to get something very similar at a low cost.
These meters provide voltage, current, and more importantly they measure how many watt hours of power moves through them. So you can look at both at the end of the day and know that your solar generated 10kWH, the batteries stored 3kWH, so you probably used 7kWH during the day - about 720w for 8 hours after losses and inverter consumption - and now only have about 3kwh/16h = 187W to use each hour overnight, and with the inverter using 30w - 60w you might only have 130w you can use overnight. With a 10% loss for conversion and wiring losses, you're looking at 110w if you want to drain your batteries down to 50% overnight - and this is all assuming the batteries are not damaged and can still hold 20kWH of power fully charged.
You should be able to get some of this from the inverter - kwh produced (from solar panels) and discharged (from batteries), by day, and total over its lifetime. You can also use the inverter's current and voltage measurements - write them down several times a day collecting the battery voltage and current, and solar voltage and current - and this will give you some insight into your power in and out. If you solar panels are hitting 250V and 6A on what you would consider a sunny day then they are only generating 1/2 their possible power. You can then investigate shading concerns, tilt/angle, system/wiring losses, inverter settings, etc. If your MPPT charge controller inside the inverter is bad it'll have a 54V and 8A output, and your panels will be generating just over 400W - 1/7 what they're meant to output, and you'll get 4kWH - 7kWH on a sunny day. It's not a small amount, but it won't charge your batteries much, and they'll run low quickly when the sun goes down.
Note, however, that the inverter's internal measurements are inaccurate. It's probably within 10% of the actual reading, but don't take its reported values as absolute truth. They are ballpark numbers. Some won't measure their internal consumption, either, so users don't complain when they disconnect all the loads and don't see 0W output.
I use separate meters (as above, except my array voltage is lower than yours so I use two of the cheap ones) and that gives me enough information to narrow down most problems (such as the MPPT controller failures I've experienced) or panel shading issues, or high load consumption issues.
Once you figure out how much energy is going into the system and how much is going out, you'll have a good idea of how much you can use overnight.
Lastly, as others have pointed out, your battery settings aren't optimized. Set the battery cut off to 48.7 (and back to grid to 48.7 for good measure), the float to 55.2, and the bulk charge to 59.2. The 1v difference may seem small, but this does make a difference in how much power you can push into the battery. These numbers are from the battery specification. The charge current isn't much of a concern. Worst case scenario, your solar array producing 3kW and you battery almost depleted at 49v then the current is 61A. Even if the battery is damaged and can only hold half its original capacity, that's still a C/4 charging rate, which is fine for these types of batteries.
That you originally had the bulk and float charging voltages at 54v and 56v - 3 volts under the battery's rating - could account for a rather substantial decrease in stored energy.
So, to sum up, your system is reasonably well matched, and adding a little more measurement and monitoring will enable you to determine whether the batteries are truly bad, or if there's something else going on with the system.