What is the ruling regarding the first Umrah in which one broke their fast due to severe exhaustion and thirst, and is it obligatory to make up that day of fasting, and what about the conflicting feelings of annoyance from the crowds and heat followed by sadness at leaving Mecca?

Your 'umrah is valid and rewarded. If you are traveling, or if fasting becomes difficult due to illness, or if you fear for your life, there is no sin in breaking your fast, but you must make up for the missed days. However, merely feeling tired does not permit breaking the fast. Wishing to leave Mecca due to fatigue is a temporary feeling that will dissipate with the believer's repentance and return to Allah.