Integrating Web Authentication with Plasmo Extension

I'm new to Plasmo and currently working on creating a Vue extension. My web application utilizes Clerk authentication, and I want to handle extension authentication based on the web session. Essentially, I aim to pass the JWT token or user data from the web session to the extension. This way, when calling any endpoint (such as implementing a comments functionality in the extension), I can use the token in the endpoint header to process the next flow from the backend/database. I've cloned the PlasmoHQ/with-vue repository and set up my sidebar and other UI components in the extension. However, I'm uncertain about the best approach to achieve seamless authentication between the web and the extension. Should I integrate Clerk into the extension project as well? Or are there alternative methods available to obtain the session from the web? I'd appreciate any insights or suggestions on the best practices and methodologies to handle this scenario efficiently. Thank you in advance for your guidance!