The former owner nicked the corner of my boat and did an ok job of fixing it but looks stupid. According to him the corner smacked the underside of the dock when a wakeboard boat buzzed by.

the picture sucks, but there’s a patch of plain white gel coat on the corner of the swim deck that I’d like to color match and feather in better. What would this process entail?

I know that's driving you nutz , trust me , but if you were (for instance) going to be re-painting the deck to make that disappear without coming back through again you'd have to grind out that gelcoat crazing all the way down to the glass and then rebuild upwards from scratch before priming.
I haven't messed with small gelcoat repairs too much but my guess is you'd have to at least dremel out all of those cracks , hoping you got them right and then pray the gelcoat you got is an exact match . Then the fun starts with the buildup and then sanding , repeat ad nauseum then buff to perfection .
It's massively tedious but it can be done.

Ah, thanks. That’s about what I expected. I had to hole saw out some engine vents and sent the cut out piece to Spectrum for a color match. It didn’t match any stock colors and they could match a custom batch for $500 a gallon. Still considering all options for now, lol.

Oh yeah , these people who 'mix things up' for a business are amazing . 2 weeks ago I needed a quart of interior latex wall paint and the minimum they could do was a gallon.
They didn't get my patronage , I improvised instead.
We can send man to the moon and back but you can't get a pint of what you need !
At least you did the best thing you possibly could have by sending them an accurate sample.

Get that sample back and send it to fgci. They will do an awesome job and it wont be 500 kicks in jewels.
i think a color matched gallon was 150 175 bucks. They code it to the customer so you can re order anytime.

https://www.fgci.com/products?pSearch=Gelcoat