There is the 2001 Authorization for Use of Military Force that a lot of the expanded War on Terror activity are nominally authorized under according to the Executive. Challenging that is up to Congress as afaik there's no standing for a random person to sue.
And Congress notably passed the dang thing and has pointedly refused to come back and limit it or curtail the admittedly expansive interpretations subsequent presidents have made of it, so I very much doubt they're going to ding a given president now.
Correct there's been several attempts to revoke or limit the 2001 AUMF and Congress has decided not to each time. It's pretty clear what is being done under the auspices of it too so failing to address the interpretation becomes a tacit endorsement at least at the institutional level. Personally I think it's been stretched to breaking but the fix is pretty simple and up to Congress.
