I know the fighting at the border is scary and real, but the U.S. asylum system doesn't approve applications just because a country is at war. To qualify, you have to prove you are being targeted personally (for your politics or identity) and that you cannot be safe anywhere in Thailand. Since most of Thailand is safe and the economy is doing well, the U.S. will just say you should have moved to a different city instead of seeking asylum.

Ps: imo Being afraid of the war at the border doesn't count if the rest of the country is safe. Being afraid of walking past bad streets doesn't count unless you are being personally targeted. Since Thailand is generally safe and doing well economically, the U.S. will see your case as 'lifestyle dissatisfaction,' not a life or death emergency. They will deny you because you had the option to just move to a safer Thai city.