Answered by Shaykh Faraz Rabbani
Does one need wudhu to read or recite the Qasidah Burdah? It says so in the preface of my copy…

Walaikum assalam wa rahmatullah,
I pray this finds you in the best of health and spirits.
It is not a legal requirement to be in a state of ritual purity when engaging in the remembrance of Allah or other spiritual works (such as reading Islamic literature or singing devotional poetry). However, it is praiseworthy to do so. [Ibn Abidin, Radd al-Muhtar]
And Allah alone gives success.
Faraz Rabbani