IF asked for at all-it will be the airline, and some are far more notorious as others for this. Notable the Gulf-based ones, like EY, EK, GF etc. You may even be denied boarding on the 2nd flite in transit.
Before covid generally cheapest low-budget tix were to KUL or sometimes PnPn, on airasia or thailionair. Just check their sites for prices now. NOTE that its not really cheap as in EUr here (I just saw ads for 2 eur tickets to Italy next winter), as they all include the 700 THB airporttax. AirAsia will reimburs this, less 200 bt fee, if not flown at all.
Also note that in general one way tix out of TH to either EUR or USA are not that cheap-in fact its most often best to buy a higher priced return with flexible return date, in case you are sure to return anyway.
And as reported above, currently the before so populair overland backpack trail is definitely completely closed-as are most other neighboring countries for casual visitors.