Is breaking one's fast for a day after having intended to fast all the remaining days until Ramadan considered a breach of covenant with Allah, and how can one atone for that, and is it permissible to break one's fast for one day occasionally in this situation?

If the vow was merely a thought and you did not utter it, then nothing is incumbent upon you, for the Prophet, peace and blessings be upon him, said: "Indeed, Allah has forgiven my Ummah for what they speak to themselves, as long as they do not act upon it or utter it."

However, if you uttered the vow, such as saying: "I vow to Allah to fast the aforementioned days," then this is a vow and an oath. If you do not fulfill it, then you must offer expiation for breaking an oath.

If your intention was to make up for fasts from Jumada al-Ula until Ramadan, then you do not break your vow by not fasting for some days during these months. Rather, the breach occurs if Ramadan begins before you have made up the fasts.

The expiation for breaking an oath is: feeding ten poor people, or clothing them, or freeing a believing slave. If you are unable to do any of these, then you must fast for three days.