I received this response from Firebase Support:
Hi there,
I'm Kevin from Firebase Support, and I'll be handling this ticket.
Are you in "read-only" mode when you experienced the issue with the
Realtime Database export? If so, there is already an internal bug
filed for this. Our engineering team is already aware of this.
However, I can't share any details for now, so I'll have this ticket
open to keep you posted with any updates.
For now, you may try to copy the URL indicated on the error page and
paste that on the browser's address bar to manually download the
exported data. You can also navigate to a deeper part of your database
and export smaller chunks.
Since you are on Blaze plan, you may also enable the Automated Backups
and download the compressed files containing the exported data.
Let me know if you have any questions.
Thanks, Kevin
I copied the link to the browser and managed to download the data perfectly.