Omega Ring Hasn't Updated Since July 14th

It looks like it hasn't been released for the Omega ring yet. Hopefully soon!

The Chromium browser was previously only available for members in the Alpha Skip-Ahead ring, but as of the last couple of days, it's not only been rolled out to Alpha members, but also Beta and Delta members. Only the Omega rings have yet to receive it.

Status July 2021

Instead of leaving the Xbox Insider program as one Ambassador has suggested you can drop down to a lower ring which receives much fewer updates. For example if you are in Beta ring drop down to Delta or Omega. The Omega ring receives the fewest updates,
usually just before it is released to the general public. This can be managed using the Xbox Insider Hub on your console.

Change the Insider preview ring your console is enrolled in.

According to the link provided above the last update for General Availability was in July.

If your console is completely turned off and power removed, your console will miss the regular system updates for the preview, usually about 600-700 MB. If you miss a preview update and another is released the complete OS system, about 4.5 GB, will need to be downloaded to ensure the console has the latest update for that preview ring.

I'm in Alpha Skip Ahead preview and manually do at least 3 updates a week.

The other preview rings have less updates each week and the Omega ring has the least.

If you don't like the constant updates to the System OS it may be to your advantage to unenroll the console from the Insiders program.

The new update is only out for some Alpha & Alpha skip ahead insiders at the moment.

If you're in the Omega ring then you'll probably be the last ring to get the update before it's released to everyone.