Use a critical section here instead of copying the items to a list. You'll need to fix up the goto err. Something like:

{
    ...
    Py_BEGIN_CRITICAL_SECTION(x);
    while (PyDict_Next(x, &i, &key, &value)) {
        ...
    }
    goto done;
err:
    Py_CLEAR(new);
done:
    Py_END_CRITICAL_SECTION();
    return new;
}

• It fails the Windows _freeze_module build (syntax errors from macro expansion).
• A version with early returns builds but causes test_str failures under free-threading on macOS/Linux

Is there a preferred pattern for using Py_BEGIN_CRITICAL_SECTION here, or would you prefer using the dict’s internal locking helpers instead?

Having the err and error labels is really confusing. We should not have both.

Having a "done" while not entirely done (that is, being done inside the function block) is confusing as well. There are too many jumps for it to be clear when reading the code. I would suggest (1) not using labels at all or (2) find better names for the labels (3) or just duplicate the Py_CLEAR(new) and remove the error label (and rename the done label). (4) wrap the logic in a separate helper.

I think @picnixz suggestion was to put the critical section outside the function. Something like:

int err;
Py_BEGIN_CRITICAL_SECTION(x);
err = unicode_maketrans_from_dict(x, new);
Py_END_CRITICAL_SECTION();
if (x < 0) {
    goto err;
}

Then inside unicode_maketrans_from_dict, the error returns can just be return -1 instead of break and no need for the if (!PyErr_Occurred()) check.