Does using the word "congregation" in a vow necessitate the presence of a congregation in the mosque, or is what matters the intention at the time of the vow?

A vow conditioned on a contingency is disliked, as the Prophet, peace and blessings be upon him, said: "Indeed, it does not avert anything, but rather, it merely extracts from the miser."

The reference point for oaths and vows is the intention of the one making the vow. If one does not know the meaning of the vow, then there is nothing binding upon them, though it is more prudent for them to fulfill it.

A vow is not contracted for what Allah has already obligated upon people, such as fasting Ramadan. Therefore, if by "congregation" you did not intend prayer in the mosque, then nothing is binding upon you. If you vowed to observe a specific prayer on Friday, then what is originally obligatory upon you is to perform all five prayers at their appointed times, and no vow is binding upon you that adds anything to that. You should engage frequently in supererogatory prayers to compensate for any prior shortcomings in the obligatory prayers.