After trying every suggestion I could find (Safari, clearing cache, different networks, different Macs), the only thing that worked was this method:

Steps:
1. On your iPhone:
• Turn off Wi-Fi.
• Use your cellular data only.
2. Install a free VPN that offers a USA (New York) server and turn it on.
3. Open Safari:
• Close all tabs.
• Go to Apple Developer.
4. Log out of your Apple Developer account.
• When it asks “Trust this browser?”, click Trust before logging out.
5. Log back in.
6. Navigate to Certificates, Identifiers & Profiles → Keys.
7. Revoke old APNs keys
(Note: any apps using these keys will need to be updated with the new one).
8. Create a new key:
• Name it something like 2025ApnYourName.
• Select Apple Push Notifications service (APNs).
• Configure for Sandbox & Production.
9. Register and immediately click Download.
• This time the .p8 file downloaded successfully. 🎉

Why this works:
It seems to be related to Apple’s server location checks and caching. Forcing a different IP (VPN to USA) over cellular, plus a fresh login, triggers the download to work.