Is the marriage valid if the guardian says, "I marry you to my ward," without full intention and merely out of tradition, given feelings of scrupulosity and doubt?

This marriage is valid, and its validity is not affected merely by uttering the offer without having the intention present, for intention is not a condition for marriage as it is for acts of worship. It is valid even if said in jest, due to the saying of the Messenger of Allah, peace and blessings be upon him: "There are three things which, whether done seriously or in jest, are taken seriously: marriage, divorce, and رجعة (return to a marriage after a revocable divorce)." Intention resides in the heart, and it is present. These are mere whispers (waswasa) and thoughts that should not be heeded. Turning away from these whispers helps in recovering from them.