Hello,
Based on the information provided it seems that Sentinel itself doesn't have permissions defined to the RG where playbooks are located. Also, the figure above seems to show permissions for 'incident-playbook' so at least for me it's unknown which permissions your own account is having. Could you share more details about the permissions set at the moment?
When you open up Sentinel playbook permissions blade you should see all RGs as from the sub (based on your permissions) as well as defined permissions to Sentinel SP underneath 'Current permissions', see figures 1 & 2 below.
If you have down-level permissions (for example Sentinel Contributor) and don't have owner permissions to all RGs you should still see the RGs but there should be mention 'No permissions. Only owner on the resource group can add permissions' at the end of the each RG.
Browse RGs
Current permissions
When you set permissions from Sentinel, it sets permissions to Entra ID Service Principal (Azure Security Insights) and you can confirm this from the RG where you're defining the permissions.
Let me know are you able to see the RGs and set permissions to Sentinel SP to the RG where playbook(s) are located. Lastly, I assume that all the resources are in the same subscription?
Here is just in case links to relevant Sentinel documentation: