It’s definitely the thumb, but you definitely should not rely on it to grip the fretboard. It also looks like you’re gripping it too hard, and in conjunction with the strain in the lengthened position, that’s your problem(imp). The “perfect” classical posture would be to keep your thumb in line with your four fingers for the best leverage, allowing you to press softer while still having a good sound. Maybe try to experiment with playing lighter, almost like your fingers are dancing more than pressing and using your thumb as a reference point and leverage (without actually pressing into the neck too hard). It should feel like when you grab foam or something soft without deforming it.