Update (Fri 6th Sep, 2024): Good news, everyone! As per Xbox's Eden Marie on Twitter, a fix has now been pushed out to rectify this issue for non-Xbox Insiders. For now though, you'll need to activate the update manually.
Original story (Mon 2nd Sep, 2024): We've come across reports over the past few days of issues with connecting to multiplayer games on Xbox following the rollout of the recent August update, and it mostly appears to affect people who have factory resetted their console.
It's not known why this is happening, but clearly it's affected enough Xbox users to generate a fuss:
To Team Xbox's credit, this is the kind of thing they'll normally fix pretty quickly, so hopefully we'll have a proper resolution very soon. In the meantime, some are reporting that by using a wired connection, the problem goes away.
We can't say we've come across this here at Pure Xbox, but then again we haven't had any need to factory reset our consoles recently! If you were thinking of doing it though, it might be worth waiting a bit longer until this is fixed...