I don't have an answer for you, but my dry cleaner used to hollar at me when I wouldn't talk to them before trying to remedy a stain multiple ways myself. She would tell me the more things i tried the less likely it was she could help because i'd helped set the stain by trying unsuccessful methods to clean the garment. Take it to your cleaners. Worst case, you decide not have them do anything. Best case, they're able to get it done.

Mould eats the fibres and dye, so it might be a permanent change I’m afraid. There are specialist mould removers but they might bleach coloured fabric.

From experience: sodium percarbonate. This is the active ingredient in oxy-clean powders and can be purchased online. In it's pure form it's commonly used as a sterilizing cleaner for brewing and bottling equipment. I've been using it in laundry for 10 years.

Maybe the dry cleaners know what to do

A little off topic, but your laundry should never be in a condition to allow mold growth. Stuff should be allowed to dry out if it got wet (if you don't intend to wash it soon) and washed laundry should be promptly dried. If you are doing that and it still happened, you might have a mold problem in your home. The shirt might not be saveable, but this might be the lesson to avoid more expensive mistakes in the future.

If it doesn't have a design on it, you could dye it a dark color with some rit dye to hide the staining.

Color-safe bleach seems to be Hydrogen Peroxide based, so you were probably safe.

Traditional Sodium Hypoclorite bleach should never be mixed with vinegar. That can release chlorine gas which is very bad for you even at low concentrations.

In general, use one cleaning agent at a time with thorough rinses in between. It can be hard to predict how cleaning agents will react. You're likely to reduce the effectiveness of them by mixing, and there's a chance of making dangerous byproducts.

What color is the shirt? You might be able to bleach it back to white if it was a white shirt. Otherwise, you might have to invest in a new favorite shirt. What made it your favorite?

Depending on what sort of shirt it is, could you considered sewing an interesting patch over the area? Take a sort of 'visible mending' approach? That way it just becomes one more memory associated with the shirt.

You could try a direct application of white vinegar to the stain, and if that doesn't seem to get it out, leaving it in bright sunlight might help. However if you're in a spot that isn't seeing much sun currently then I definitely second the suggestion to take it to a dry cleaner's.