Is it permissible to exaggerate in praising oneself and joking about it with friends by saying "I am a scholar" or "deeply knowledgeable" with the intention of laughter, knowing that everyone is aware of this?

There is no harm in jesting if it is free from falsehoods such as backbiting, slandering, and lying. The Prophet, peace and blessings be upon him, used to jest, and he would only speak the truth. Moreover, some Companions and Successors used to jest without indecency, lying, or backbiting. Reprehensible jesting is that which is mixed with one of these characteristics, or in which there is self-praise. Jesting should be for the purpose of entertaining companions and showing affection to those one interacts with, or to relieve distress. However, jesting should not lead to immodesty or insult, nor should it be used in matters of religious rulings.