Now I have this side of the logic figured out. But thing is for some reason. This structure completely ignores the Bearer Token.

You are correct. Please take a look at this https://github.com/dotnet/aspnetcore/blob/main/src/Security/Authentication/JwtBearer/src/JwtBearerHandler.cs#L74, it is the reason. I believe you can understand why it ignore Bearer Token in Authorization Header: the logic for loading token is skipped because you set token at OnMessageReceived event.

Btw, I see your design is a little bit weird, why you set Refresh Token to auth_token cookie, and OnMessageReceived set token from auth_token as refresh token to authenticate (instead of access token). Please clarify your purpose first.