be busy Ving (acceptable)
be busy with n. (acceptable)
?be busy with Ving (questionable)
https://reurl.cc/93L2Gd
https://reurl.cc/QEGzeo
https://www.usingenglish.com/forum/threads/busy-with-doing.303102/
https://forum.wordreference.com/threads/busy-with-ving.3337505/
https://forum.wordreference.com/threads/busy-in-ving.3336505/