This comes up repeatedly so here is comprehensive guide to non-stick coatings and how it pertains to your wok.
Unless your non-stick coating is ceramic, it is most likely coated in a material called polytetrafluoroethylene, or PTFE for short. More commonly known under the brand name Teflon, PTFE is an industrial plastic. It has near the lowest friction coefficient of any material known to man which is what gives non-stick pans their non-stickiness. It is extremely inert and will not react with acids, bases, alcohols, and other solvents. It has good heat resistance relative to most plastics. That combination of properties makes it excellent for manufacturing, and an effective coating for cookware.
Where PTFE starts to fail is in durability. It is just plastic, after all, categorized as a medium-soft material. Mishandling it will damage it. Scraping hard material like metal utensils or other pans against it will cause plastic to break off, which may end up in your food. If you can see visible damage to the non-stick coating, it is no longer safe to use and should be thrown out.
The temperature range, while high for a plastic, is still only 500° F. That's well below what a common household stove can reach and lower than you want for many stove top cooking techniques. Once overheated, PTFE will start to break down and release toxic gases into the air. These gasses cause flu-like symptoms in humans and are very quickly lethal to birds. After being overheated, a PTFE coated pan should be thrown out. You can't undo the damage.
Perfluorooctanoic acid (PFOA) is a chemical that used to be used in the process of manufacturing PTFE cookware. It is classed as a carcinogen and has a very long half life in your body after ingestion. In the US, all cookware sold since 2015 is required to be PFOA-free; if you have a modern non-stick pan PFOA should not be a concern.
If you bought a non-stick wok and the coating is damaged, you may encounter people who suggest you can strip the coating off to make it bare carbon steel. While technically possible, it's not recommended. Since PTFE is so inert, chemical stripping is not an option. You could heat it until it flakes and scrape it off, but it must be done carefully outdoors and there's no data on what may or may not leech into the metal while PTFE is breaking down under high heat. You could machine it off, taking a small layer of metal with it, if you have access to the right equipment. But when a nice carbon steel wok can be had for under $40, that seems like an awful lot of work.
To conclude the fact portion of this post, when handled correctly PTFE is considered safe to cook on and even safe to ingest. It is one of the most inert chemicals known and should pass through your body with no ill effects. It has even been tested as a filler food to assist people in not overeating.
That said it is still a plastic. In my humble opinion, the care required to maintain it is not worth the convenience of the additional non-stick properties over cast iron, carbon steel, or stainless steel (aluminum is a topic for another time). It is far too easy to accidentally overheat a pan while prepping other food while it preheats. Unless you're monitoring it carefully with an infrared thermometer then you likely have no idea if your pan has ever been overheated or not. Most of my stove-top cooking involves high heat searing so non-stick pans would be of very little use to me even if I did have one to care for.
I really can't make peace with the idea of cooking on and ingesting plastic no matter what the studies say. Part of that may be that I work with it in an industrial setting so I'm hyper-aware of the fact that a sheet of PTFE doesn't look much different than PVC. Nothing about that makes me want to cook on it or ingest it. When all the iron atoms are gone from the earth, then maybe I'll consider it. Until then my cast iron and carbon steel will pull their weight just fine.
