Tire plug kit. Did it several times when I was younger. They’re 💯 safe and will be effective. I don’t do it anymore only because the shop I get tires at offers lifetime patching for free. Yes–you need to do it or the air will slowly leak out giving you poor mileage, at worst a blown tire while you’re driving on the freeway.
It’s gone. Leave it? You’ll end up in the side of the highway at the worst time. Maybe at night snowing
Buy a tire plug kit off Amazon, and plug it yourself. People will bash me for this, I’ve done it, used tires for years that were plugged, and never had a problem. There will always be exceptions. If you take it to a tire store, they should be able to use a plug patch, as it looks far enough away from the side wall of the tire, which will be better than a plug alone.
I’d probably use a rope plug. I use extra glue with it and none have failed me yet. Most tire makers won’t approve of them tho.
Needs to be removed and plugged