Betta fish fin rot?

Hi everyone,I'm worried my female koi betta is getting fin rot. I'll attach pictures from October 22nd and from today. Last week she was having trouble breathing so I did a 50% water change on thursday, and a 75% water change and thorough gravel vacuum +tank wall wipedown on Friday. I had to leave her over the weekend but her breathing had calmed down. The other thing is, I leave her with an automatic feeder over the weekend for Saturday and half of Sunday, but I'm not sure if she even registers that it is there and actually eats the couple of bug bites that it drops in. She seemed stressed when I first got in this morning, very fast swimming and glass surfing but seems to have calmed down after I fed her and moved away from the tank. I have seachem polyguard - should I dose with that? Also in general her fins have always been a little patchy - Ive just attributed that to her fins growing (I've had her for 4 months).


Tank details:
Size: 20 gallon long
Inhabitants: 1 betta fish, some ramshorn snails, about 10 blue dream shrimp
Other stuff: driftwood, dragon rock, various live plants, 2 plastic tunnels, 1 ceramic hide
Water quality: Ammonia 0, Nitrite 0, Nitrate 5 ppm
Cleaning regime: ~30% water change once a week , vacuum substrate, and once in a while I squeeze my filter media in the old tank water, dechlorinate with seachem prime.
Filter: HOB with a super old carbon cartridge and some sponges
Water temp: 80 degrees
Feeding: 5 frozen brine shrimp twice a day, fasting day on Sunday, sometimes I do bug bites and once a week I do frozen bloodworms.
Plant fertilizer: I dose the tank every few days with this fertilizer, I always check nitrates to make sure I'm not overdosing with the fertilizer (because I did that once)

Hi everyone, I just wanted to bump this because I'm concerned it's getting worse. I'm attaching two close ups of her tail, if anybody could let me know if this is fin rot I would really appreciate it!

You can try dosing with aquarium salt for a couple of weeks to see if this helps. Im copying this advice from @Colin_T Re adding salt:

SALT
You can add rock salt (often sold as aquarium salt), swimming pool salt, or any non iodised salt (sodium chloride) to the aquarium at the dose rate of 1 heaped tablespoon per 20 litres (5 gallons) of water. If there is no improvement after 48 hours you can double that dose rate so there is 2 heaped tablespoons of salt per 20 litres.

Keep the salt level like this for 2 weeks. If there's no improvement after 1 week with salt then you should stop using it and look at a chemical based broad spectrum medication that treats bacteria and fungus.

The salt will not affect the beneficial filter bacteria, fish, plants, shrimp or snails.

After you use salt and the fish have recovered, you do a 10% water change each day for a week using only fresh water that has been dechlorinated. Then do a 20% water change each day for a week. Then you can do bigger water changes after that. This dilutes the salt out of the tank slowly so it doesn't harm the fish.

If you do water changes while using salt, you need to treat the new water with salt before adding it to the tank. This will keep the salt level stable in the tank and minimise stress on the fish.

When you first add salt, add the salt to a small bucket of tank water and dissolve the salt. Then slowly pour the salt water into the tank near the filter outlet. Add the salt over a couple of minutes.