If you are using solid-node-client you are already using an OIDC, it happens behind the scenes. When you login, the server sends an OIDC DPoP token to solid-node-client which it stores and sends back to the server with each fetch request from solid-node-client.
Is there anything wrong with my local NSS settings given above screenshots I should be worried about?
Please go to solid/node-solid-server - Gitter and ask your questions there. I don’t know enough about local hosting NSS to answer.
Could you try a multi user settings.