This is the same issue described in MCPE-102459 (https://bugs.mojang.com/browse/MCPE-102459?focusedCommentId=1081092&page=com.atlassian.jira.plugin.system.issuetabpanels%3Acomment-tabpanel#comment-1081092).
I was not able to download from the Minecraft store the mash-up packs that came included with the Minecraft starter pack for PS4; however, I was able to download them from settings/resource packs instead of the store. After buying new worlds in the marketplace, I get same error about not having "enough space" even with only 5 worlds of 300mb and nothing else. I have multiple terabytes of free space. I just installed the latest update 2.33 and didn't make a difference.
The support team asked to reinstall the game, now it is worse. I can not re-download many of the store purchases that were working before. Please stop pointing people to reinstall the game.
Related issues
Comments

If you know an issue has already been reported, please do not create a new report.