In "man open_tree":

As with "*at()" system calls, fspick() uses the dirfd argument in conjunction

You meant "open_tree"

If flags does not contain OPEN_TREE_CLONE, open_tree() returns
a file descriptor that is exactly equivalent to one produced by open(2).

Please, change "by open(2)" to "by openat(2) with O_PATH" (and other similar places).

--
Askar Safin
https://types.pl/@safinaskar