Toto toilet that keeps running after flush and won’t fill unless I jiggle handle, how can I fix it? video included

[Rockstead]

Toto model is CST 604CEFG

I’ve had it for a few years and it’s worked without issue but in the past month or so it has the issue that you can see in the video.

If I jiggle the handle it seems to fix for a little while.

Can I fix this myself without a plumber? What would I have to replace and what tools would I need? A video reference would be great.

https://imgur.com/a/6N6pVBJ

If it’s a matter of replacing the flapper, is there a quality difference between a genuine Toto flapper that I can order off of Amazon vs a part that is made to fit from a different manufacturer found in my local hardware store, I.e. Korky Genuine TOTO Toilet Flapper, 3-in

Or should I try cleaning the flapper first? Could that be why as well, I’ve had these for around 5 years easy.

Thanks for any help.

 

[Tuttles Revenge]

The flapper looks like its old. The color looks really faded. I can't attest to which brand, but it likely needs replacing.

BTW, the chain also looks like its adjusted properly, with no tension pulling up on the flapper. Does it always fall down with no tension? Sometimes the chain will get hung up on the flapper. That straw piece is there to prevent the chain from catching up on the flapper, so its less likely the cause.