Borrowed time.

[Mr Celine]

Conti recommend 80psi no matter what your weight is. 60 should have been fine for mine.
Do I contact their customer services & see if they’ll replace it?

If you don't ask you don't get.

It could be a manufacturing fault. There is a noticeable bulge in your tyre with what looks like a minor mark on the sidewall.
Mine isn't a very good comparison as it's a clincher, but even with obvious damage including broken threads the tyre is still the right shape.

 

[iluvmybike]

I and OH have ridden with Conti GP4000s on all four of our road bikes for years and never had any issues fwiw. Several thousand miles out of every tyre...

 

[Ajax Bay]

I’ve probably had too much pressure in rather than too little.

Whose "too much"?

Conti recommend 80psi no matter what your weight is. 60 should have been fine for mine.
Do I contact their customer services & see if they’ll replace it?

Why do you think 60psi is enough? How wide is this GP 5000 TL? What load do you think is going on the rear wheel?
I would look on the inside of the tyre where the damage can be seen and see if there's signs of delamination or thread separation. If there is, replace.
Ref customer services: I would not waste my time or theirs.

 

[Milzy]

Whose "too much"?

Why do you think 60psi is enough? How wide is this GP 5000 TL? What load do you think is going on the rear wheel?
I would look on the inside of the tyre where the damage can be seen and see if there's signs of delamination or thread separation. If there is, replace.
Ref customer services: I would not waste my time or theirs.

I believe 60 psi is enough for a 10 stone rider on 25mm. Could be wrong.

 

[Ajax Bay]

I believe 60 psi is enough for a 10 stone rider on 25mm. Could be wrong.

That's rather low, imo, and I would expect snakebites if running with tubes. 10 stone is 64kg. Add bike and clothing to get load overall of 74kg (say) and the rear will take 60% of that = 44kg. Look at this authoritative BQ article and you'll see that, for that load and a genuine 25mm wide tyre (quite often 25-622 measure less), about 85psi is recommended. 60psi would be fine for the front. If your style is more randonneuring as opposed to 'racing', then the rear/front ratio is 55%/45% and use the graph in the article.
It may be that running tubeless you don't puncture but at lowerpressures a hard pothole or street furniture interface may damage the sidewalls of the TL tyres - and this maybe is what's happened.