Are the Xbox One and Xbox Series X/S fully compatible for multiplayer over network games?

I am unable to connect a Halo CE (anniversary edition) session on a Xbox One console to the game running on a Xbox Series S console. Network is local (within my home).

From the Xbox One, player NUNYA_001 can send a join game invite to a player on the Series S. On the Series S player NUNYA_999 cannot join the game (option to join a party is available but not join a game). From within the Halo CE game lobby Missions on the Xbox One console I can see NUNYA_999 in the friends list but the text above the player's information is grayed out. If I select NUNYA_999 on the Xbox One the menu appears but the "JOIN PLAYER" button is grayed out.

NUNYA_001 can send an invite to NUNYA_999 from the players panel in the roster (button above "JOIN PLAYER") on the Xbox One but the only option available to NUNYA_999 on the Series S is "JOIN PARTY" (not game).

Behavior is pretty much the same if I host the game on the Series S; NUNYA_999 can't select "JOIN PLAYER" for NUNYA_001.

Both gamers have Game Pass.

Does anyone have a solution for this problem? What am I missing?

Internet searches have only provided a lot of irrelevant information.

:)