Unable to download new purchases from marketplace. "Downloading..." but never proceeds or completes.

I'm unable to download new purchases from the marketplace in Minecraft 1.18.31 on a 6th generation iPad running iPadOS 15.4.1.

I had previously been able to download purchases.

The issue started when I purchased a new world ("Skyblock Space Wars"):

• I saw the "Purchase in progress. This shouldn't take long." dialog.
• I clicked on the "Download" button next to the world.
• I clicked on the "Download" button in the confirmation modal.
• I saw the download progress modal - "Step 1 of 2 - Downloading Content" - but the progress bar never moved and the modal never updated.
• I clicked the 'X' to close the modal.

Now:

• In Marketplace > My Content > Owned, I see the world with the status "Downloading..." but the download never proceeds or completes.
• I'm unable to download other purchases, including worlds and texture packs. I get the same behavior for the other purchases as I do for the first world above.

Things I've tried unsuccessfully:

• Waiting. (It's been several days. This isn't a temporary marketplace outage.)
• Connecting to different wifi networks and ensuring we have Internet access.
• Restarting Minecraft.
• Logging out and logging back in.
• Restarting the iPad.
• Clicking the "Restore" button on the world. (It showed the "Restoring your purchases!" dialog, but it didn't change anything.)
• Changing my avatar. (Someone suggested this could fix marketplace problems.)

Things I haven't tried:

• Reinstalling Minecraft. (I'm worried we'll lose our worlds. My son will lose his mind if that happens.)

Other observations:

• When I first start Minecraft, the marketplace button is disabled for several seconds and has a red exclamation mark next to it. After several seconds the red exclamation mark disappears and the marketplace button is enabled. I don't see this happen on our other devices.