1) I know that Approach to is a preposional phrase that it requires a present-participle verb following it.
Comment: No, approach to is not a prepositional phrase. It is a noun plus to. /His approach to explaining this problem is straight forward/.
2) He approach to transitioning students from high school to university
But, why not going to?
Comment: approach as a verb: He approaches students transitioning from high school to university. No /to/.
Compare the verb form to the noun: His approach to teaching is very old fashioned. Approach as a verb does not take to: They approached the man from behind.
I'm going to meet you.
Aren't they the same transitive verbs and used to express a movement or moving action? How can I actually use the "to" as an infinitive marker or preposition?
Answer: No, in the form /going to + verb/, going to expresses a future.
I'm going to leave now. It is not introducing a prepositional phrase.
Summary: going to expresses a future and is followed by any verb: going to see, going to do, going to think
approach as a verb does not take /to/. Approach as a noun takes to but is not a prepositional phrase. It's just a preposition used with the noun: A person's approach to life. It is used to show a direction or purpose.