I work on this issue to fix it.

Are you still working on this @hakancelik?

Yes I will send pr soon.

@DahlitzFlorian it looks like a PR was submitted August of last year : #21849

I've made the few additional changes to those in this PR. When I work out the issues, I'll make a new PR. I took out an attempt with path_t. However, here is why I think argument clinic (or something else?!) is actually intercepting the attempted call:

With my temporary debugging, I have this function in [Modules/_gdbmmodule.c](https://github.com/python/cpython/blob/main/Modules/_gdbmmodule.c):

[clinic start generated code]*/

static PyObject *
dbmopen_impl(PyObject *module, PyObject *filename, const char *flags,
             int mode)
/*[clinic end generated code: output=9527750f5df90764 input=812b7d74399ceb0e]*/
{
    PyObject_Print(filename, stdout, 0);
    printf(" from _gdbmmodule.c (XXX)\n");
    /* ... rest of function ...*/

And I have a very simplified test script:

import _gdbm
import sys
from pathlib import Path

print(sys.version)
path = '/tmp/tmp.db'

db = _gdbm.open(path, 'c')
print("Opened with string path")
db.close()

db = _gdbm.open(Path(path), 'c')
print("Opened with path-like")
db.close()

The output of running this is:

3.11.0a0 (heads/[bpo-45133](https://bugs.python.org/issue45133)-dirty:0376feb030, Sep  8 2021, 00:39:39) [GCC 10.3.0]
'/tmp/tmp.db' from _gdbmmodule.c (XXX)
Opened with string path
Traceback (most recent call last):
  File "/home/dmertz/tmp/pathlike-dbm.py", line 12, in <module>
    db = _gdbm.open(Path(path), 'c')
         ^^^^^^^^^^^^^^^^^^^^^^^^^^^
TypeError: open() argument 1 must be str, not PosixPath

So before I get to the first line of the _gdbm.open() function, the TypeError is already occurring when passed a PosixPath.

If anyone wants to look at my not-yet-complete changes (see other comment), it's https://github.com/DavidMertz/cpython/tree/bpo-45133. It has a different bpo because I filed a duplicate before realizing. I can change the branch name before a PR, but making it work is the more important issue.

New changeset 707137b by Henry-Joseph Audéoud in branch 'main':
bpo-40563: Support pathlike objects on dbm/shelve (GH-21849)
707137b

Thank you for your contribution, Hakan, Henry-Joseph.

Sorry, David, there was already a PR, and it was not dead, it just waited for a coredev review.