I have experienced this three times in the last week so it seems fairly reproducible.

While the Xbox is updating a different game (e.g. Sea of Thieves) in the background, Minecraft consistently shows "unable to connect to realms". A few seconds after the other game finishes updating, Minecraft can once again connect to my realm.

During this time I can still connect to the realm with a different client (e.g. my Android phone) so it seems like an Xbox client issue.