Is fearing leading the second congregational prayer in the mosque – due to apprehension of people’s requests for it and a desire for solitary prayer to prolong it – considered hypocrisy?

You are afflicted with waswasah (whispers/obsessive thoughts), so you must cast them aside and ignore them. Your eagerness for the first congregational prayer is a good thing, not riyaa' (showing off). If you are asked to lead a second congregation and you are the most knowledgeable among the people, then lead them in prayer and be light. The difference between being light in leading prayer and prolonged in solitary prayer is in accordance with the Sunnah. Your prayer with a congregation outside the mosque fulfills the obligation, but be keen to attend the congregational prayer in the mosque to seek its virtue and to avoid disagreement. Abandon these waswasah and proceed with your worship, striving for sincerity.