Is Umrah considered valid if a feeling of ostentation (riya') was mixed in a part of the sa'y (the ritual circumambulation between Safa and Marwah), and then the phrase "I don't care if Allah accepts it or not; the important thing is that I performed Umrah" was uttered due to distress? And does the noble Hadith "Leave that which makes you doubt for that which does not make you doubt" apply to this situation?

Your Umrah (definition) is valid, and your distress and fear of showing off (riya') are signs of your sincerity. This is the state of believers who fear that their deeds may not be accepted. Your inner thoughts contain no sin, as they are merely self-talk. We advise you to frequently supplicate for the acceptance of your Umrah and all other good deeds, and not to surrender to excessive whispers (waswasah) and fear. Combine fear with hope, and have a good opinion of Allah, for He has promised to accept righteous deeds. He said: "{And He will not deprive you of [the reward of] your deeds}" and "{So whoever does righteous deeds while he is a believer - no ingratitude will be shown for his effort, and indeed, We are writing it down for him}" and "{Indeed, We will not allow to be lost the reward of any who did well in deeds}."