In Python 3.10 it is no longer possible to create an exception type that inherits from both OSError and AttributeError. This has worked in Python 3.9.
I don't see anything in changelog/release notes that would suggest it being intentional.

Behavior in Python 3.9:

Python 3.9.2 (default, Feb 28 2021, 17:03:44) 
[GCC 10.2.1 20210110] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> class C(OSError, AttributeError): pass
... 
>>> C
<class '__main__.C'>

Behavior in Python 3.10:

Python 3.10.0 (default, Oct  4 2021, 00:00:00) [GCC 11.2.1 20210728 (Red Hat 11.2.1-1)] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> class C(OSError, AttributeError): pass
... 
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: multiple bases have instance lay-out conflict

My (very) wild guess is this being related to https://bugs.python.org/issue38530

You are correct. To be more precise, it's caused by #61060. The commit introduced PyAttributeErrorObject struct. Since AttributeError and OSError now have an incompatible memory layout, it is no longer possible to create a subclass that has AttributeError and OSError as parent classes.

Unfortunately there isn't much we can do here other than document this :(

Also, just to clarify something: there is no guarantee that multiple build-in, unrelated exceptions can be inherited and this is not supported. And this is not unique to this case. For example:

>>> class A(StopIteration, OSError):
...    ...
...
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: multiple bases have instance lay-out conflict

>>> class A(SyntaxError, OSError):
...    pass
...
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: multiple bases have instance lay-out conflict
>>> class A(ModuleNotFoundError, OSError):
...    ...
...
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
TypeError: multiple bases have instance lay-out conflict

Suggestion: At the end of https://docs.python.org/3/bugs.html, add

"Creating a subclass that inherits from multiple exceptions may not work and the potential conflicts may change in new versions."

Suggestion: At the end of https://docs.python.org/3/bugs.html, add

Hummm, I am not sure that page is the most adecuate for this, no? That is how to deal with bugs in general, not about specific bugs.

More specific would be "Inheriting from multiple exceptions may fail due to instance layout conflicts. Such conflicts may depend on the Python version." This would effectively say "Don't bother reporting layout conflicts -- we know about them and they are not bugs." while not discouraging reports of other problems.

New changeset dff0b71 by Łukasz Langa in branch 'main':
bpo-45464: [doc] Explain that subclassing multiple exceptions is fragile (GH-29094)
dff0b71

New changeset b2a9899 by Miss Islington (bot) in branch '3.10':
bpo-45464: [doc] Explain that subclassing multiple exceptions is fragile (GH-29094) (GH-29104)
b2a9899

New changeset 427ab12 by Miss Islington (bot) in branch '3.9':
bpo-45464: [doc] Explain that subclassing multiple exceptions is fragile (GH-29094) (GH-29105)
427ab12

Marking this as "wont fix" since only documentation was updated. Thanks for reporting, Marek!