For anyone also still having this issue, I got it working by creating a 'NuGet' service connection instead of 'Azure Repos/Team Foundation Server'
Make sure to fill in the 'Feed URL' field with the link that Azure Artifacts provides when you select "Connect to Feed" and the "NuGet" option in the Azure Artifacts tab.
The PAT token you create for the 'Personal Access Token' needs have Package read permissions and it needs to be created on the organization that's hosting the Azure Artifacts feed.
I provided a link from Azure Documentation that goes into detail on how to publish a NuGet package onto another Azure Artifacts feed.
https://learn.microsoft.com/en-us/azure/devops/pipelines/artifacts/nuget?view=azure-devops&tabs=yaml
This link is for publishing, so the permissions given were for publishing, to read just simply change those to read, like I previously mentioned.
