Parallel function saving and reading it back using PETSc or adios4dolfinx

adios4dolfinx does nothing special. It uses standard MPI neighbourhood communicators.
The snippet I posted above is an illustration of what happens internally in adios4dolfinx in the call you are referring to.

It could be related to: Find cell tags from two overlapped meshes with different resolutions - #11 by dokken
but it is hard for me to work with when I cannot reproduce your error.