Is there any proof that Budai was an actual historical figure
There is research and writing to proof Budai monk is a historical figure around 10th century and under category of Buddhism Zen teaching.
The source found that seems not having enough of a specified quality and could not be suitable to Junior Buddhist.
&quot;The sources available to modern scholars concerning Pu-tai' s life are deficient&quot;. The materials give merely a nebulousaccount,  all  are  agreed that he was  a mysterious  cleric whoperformed  miracles.
Reference
https://wikivisually.com/wiki/Budai
Hsiao, Bea-Hui (1995) Two images of Maitreya: Fu Hsi and Pu-tai Ho-shang. PhD thesis. SOAS University of London.
https://eprints.soas.ac.uk/28925/