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.

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.

Needs to be removed and plugged

It’s gone. Leave it? You’ll end up in the side of the highway at the worst time. Maybe at night snowing

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.