Is there any proof that Budai was an actual historical figure Does any online site refer to evidence that this monk ever existed as an actual historical figure? If the person is believed to be so important and famous as next Buddha then where is the tomb?
Refer to wikipedia

Many Chinese Buddhists believe he was a reincarnation of Maitreya, the person who will become the next Buddha after Gautama Buddha.
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/