The endpoint: https://apis.roblox.com/asset-delivery-api/v1/assetId/
Does not properly authenticate users of a group. It is only accessible to the original owner of the asset.
More info in this thread: API Endpoint refusing access to some users in group
Affected URL: Legacy overview | Documentation - Roblox Creator Hub
These are legacy endpoints and unlikely to be changed. In the thread you linked you discovered that authentication with this endpoint works if users have the correct legacy permissions. Nowhere in the affected URL does it state what permissions users need to properly access this endpoint.
It could be useful to include this information, but it’s likely that if doing so the other legacy endpoints will require the same information. I’m not entirely sure this is something that needs to be changed though, as again this is a legacy feature…
Just to note, this isn’t really a ‘true’ legacy API / feature; this endpoint still has the same stability guarantees as OpenCloud.
All endpoints on this page use the same stability guarantees as the Open Cloud v2 and v1 APIs and are currently Beta. Beta endpoints are ready for public use. Breaking changes are possible but rare.