Prepositional/infinitive phrase connectors

When prepositional /infinitive phrases are used as sentence connectors i. e they come at the beginning of the sentence, what is their status in the sentence. Are they mere connectors and not a part of the sentence or they also are integral part of the sentence they introduce.

Example:- He is a hardworking man. Apart from this, he is also very diligent. Here “apart from this” is only a connector or also integral part of the sentence “he is also very diligent.

Similarly, “He wants to be rich. To achieve his objective, he is working very hard.Here “To achieve his objective”is only a connector or also an integral part of the sentence “he is woking very hard” acting as adverbial.