Another nail biter here...
It does sound as if you are (understandably!) frustrated that he's doing something with his body that you strongly believe he shouldn't.
If he doesn't want to stop, realistically you can't force him. He will wash off anything you put on his nails or bite them anyway and put up with the bad taste. He'll do it at night when you can't monitor him etc
At 13 and if he's stubborn there's a danger of turning it into a battle ground and he'll become more entrenched.
Anecdotal evidence here (!) but My step mother spent years trying to force her children (my step and half siblings) to stop with loads of methods and none were effective. My DM just ignored me biting mine! As adults we are all still nail biters, they are 'worse' than me in that I can (and have) stopped on occasions and don't bite them down to the quick the way they do...
I've seen suggestions that you try and limit manage biting rather than stopping it. E.g. say it's not appropriate in certain situations or ask child to try and stop one nail at at time (or one hand, or whatever), insist on keeping hands clean and put plasters over any that are looking sore or damaged, keep a nail file and clippers handy to cut any ragged edges that are tempting to chew
That might work if he's willing to co-oporate and wants to stop...
For me it's when I'm bored more than stressed but everyone has their own triggers.