Is it obligatory to fast the vow that entails fasting three consecutive months, which was vowed to be during the engagement period, if the marriage contract and wedding took place on the same day and there was no engagement period, knowing that I am currently pregnant and unable to fast, and is it permissible to pay a monetary expiation instead of fasting?

A vow contingent on a condition is disliked (makruh), but it must be fulfilled if the condition is met, based on the Prophet's (PBUH) saying: "Whoever vows to obey Allah, let him obey Him."

Therefore, if you vowed to fast three consecutive months upon marrying a specific person, you must fulfill it, as the marriage has occurred.

If you are unable to fast now, or if fasting is difficult for you, you may postpone it until you find a suitable time, or until your excuse is removed if its removal is hoped for.

However, if your excuse is not expected to be removed, you must perform an expiation (kaffarat yamin): feeding ten poor people, clothing them, or freeing a slave. If you cannot find any of these, then fasting three days.

Your statement "and the fasting would be during the engagement period" does not affect the obligation to fulfill the vow, because the intention was the occurrence of marriage. Unless you meant that the vow is only binding if there was a period between the engagement and the marriage and this period did not exist, then in that case, nothing is binding upon you.