What is the max allowed depth for bip32 derivation paths? Generally I see that bip32 derivation paths are something like m/1/2/3/4, etc

How deep is allowed? Is there a limit on how deep the tree can go?
A path can have, at most, 256 elements, including the master. This limitation comes from the extended public key serialization format's depth field. This field is a single  byte which means it only has 256 possible values.