Hello @Abhishek_Agrawal and thank you for your question.
I do not believe your ask is possible at this time.
Bearer tokens expire, so putting the bearer token in the Linked Service does not work.
You are correct in noting that Bearer token is not one of the options in the linked service. The way to authenticate with bearer token, is first select Anonymous as the authentication option. Then, in the copy activity, add additional header "Authentication", and use the Bearer token in the value.
You get new Bearer tokens by first using a Web activity to the authentication endpoint with your credentials.
In your wording, it sounded like you mainly wanted to avoid making web calls to the Key Vault. Is this the main issue, or have I misunderstood your ask?