From upstream tracker (Igor Fedotov):

Well, some more findings on the issue:
1) Apparently this issue is present in Pacific minor releases 16.2.6 through 16.2.9
Not sure about earlier ones but it definitely does not exist in Quincy and main branch.

2) After comparing the delete version operation's behavior between Quincy and Pacific I realized that RGWRados::get_obj_state_impl() function gets different object reference (rgw_obj& obj). In Pacific obj.key.get_oid() call result lacks proper object version specification (while it's present originally at RGWDeleteObj::execute()) and this finally causes ENOENT return from get_obj_state_impl().

More investigation reveals the following implementation of
int RGWRadosObject::get_obj_state(const DoutPrefixProvider *dpp, RGWObjectCtx *rctx, RGWBucket& bucket, RGWObjState **state, optional_yield y, {
rgw_obj obj(bucket.get_key(), key.name);

return store->getRados()->get_obj_state(dpp, rctx, bucket.get_info(), obj, state, follow_olh, y);
}

which is apparently a culprit as it makes an incomplete object reference which lacks version ref.
And indeed Quincy release implementation is different: {
return store->getRados()->get_obj_state(dpp, rctx, bucket.get_info(), get_obj(), state, follow_olh, y);
}

Updating to the latter implementation fixes the bug for me.
But I'm not completely sure this is 100% corrent and there are no side effects.