Yes, it is correct that the hadith related to the supplication you mentioned is da'eef (weak):
حَدَّثَنَا مُسَدَّدٌ، حَدَّثَنَا هُشَيْمٌ، عَنْ حُصَيْنٍ، عَنْ مُعَاذِ بْنِ زُهْرَةَ، أَنَّهُ بَلَغَهُ أَنَّ النَّبِيَّ صلى الله عليه وسلم كَانَ إِذَا أَفْطَرَ قَالَ: اللَّهُمَّ لَكَ صُمْتُ وَعَلَى رِزْقِكَ أَفْطَرْتُ
Narrated Mu'adh ibn Zuhrah: The Prophet of Allah (ﷺ) used to say when he broke his fast: O Allah, for Thee I have fasted, and with Thy provision I have broken my fast.
— Sunan Abi Dawud — Hadith 2358
As the reference above says, this hadith was ruled as weak by Muhammad Nasiruddin al-Albani.
The chain of narration is clearly severed, as it is basically saying that Mu'ath ibn Zohra was "informed" (in the Arabic chain of narration quoted above), but it neither mentioned whether this was in a form of narration (repeating the exact words of the Prophet ﷺ, not paraphrasing), nor did it mention who informed Mu'ath. Abu Dawud documented it in his Sunan, but he also documented it in his Maraseel (hadiths with severed narration chains).
This hadith was also documented in other books (Musannaf ibn Abi Shaiba, al-Baihaqi, etc.) through the narration of Mu'ath ibn Zohra, but without the use of the word "informed". Nonetheless, Mu'ath ibn Zohra is a tabi'i (one generation after the companions), and is not known to be trusted (or untrusted, for that matter; just not well documented). This makes the hadith mursal (severed narration chain).
This opinion is shared by Ali ibn Abd-al-Malik al-Hindi, Ibn Abi Hatim al-Razi, Ibn Hajar al-Asqalani, Muhammad al-Bukhari, Umar ibn Muhammad ibn al-Mulaqqin, Yahya ibn Sharaf al-Nawawi, and Yusuf ibn Abdur-Rahman al-Mizzi.
You can refer to Mer'aat al-Mafateeh pp. 475, Hadith 2014 (Arabic only) for more information.