From this passage, did Jesus do miracles after all?
Yes, as per John 2:23, but at his time and place.
Why didn’t Jesus commit to them if they believed in His name?
They believed in His name as that of a healer, but they didn’t see the healings as the sign of his deity. Jesus knew that those who desired and believe in just the miracles will not truly believe Him for who He is. He doesn’t want someone who just wants a genie who grants them their wish. He wants people who want to have an intimate, personal relationship with Him for who He is - the creator of the universe, including us - and for what He already did for us 2000 years ago.