Is the Ramadan fast suspended between the heaven and the earth and not raised except by Zakat al-Fitr?

A weak hadith has been narrated from the Prophet ﷺ stating that the month of Ramadan is suspended between the heavens and the earth and will not be raised to Allah except with zakat al-fitr. This hadith has been deemed weak by Al-Suyuti, Al-Manawi, and Al-Albani.

The reason for its weakening is that if the hadith were authentic, it would mean that the acceptance of the Ramadan fast is contingent upon giving zakat al-fitr, which is not stated by any scholar.

It is authentically reported in Sunan Abi Dawud, on the authority of Ibn Abbas, may Allah be pleased with them both, that the Prophet ﷺ enjoined zakat al-fitr as a purification for the fasting person from idle talk and obscenity, and as food for the poor. This hadith explains the wisdom behind zakat al-fitr, indicating that it remedies deficiencies in fasting, but it does not mention that fasting is not accepted without it.