What is the ruling on the whispers of self-admiration (ʿujb) and showing off (riyāʾ) during prayer, and resisting them by saying, "It's almost over, just one more rak'ah and I'll finish," or by feeling happy for not paying attention to Satan?

The cure for intrusive thoughts (waswas) is to ignore them and pay no attention to them. So, repel them whenever they come to you and do not care about them. These intrusive thoughts do not affect the validity of your prayer, and there is no harm in your joy when repelling them and not giving in to them.