Minecraft Bedrock music can't be downloaded/updated from the store, without a Microsoft account. You can get anything else that's free in the store without logging in, but not music, despite both being marked "free".
This was an issue since the in-game music was first introduced.
Thank you for your report!
We're actually already tracking this issue at MCPE-71081, so I will resolve and link this ticket as a duplicate.
If you would like to add a vote and any extra information to the main ticket it would be appreciated.
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