By browser extension I mean WebExtension https://developer.mozilla.org/ru/Add-ons/WebExtensions.
I tried to use it for just local files and got:
Access to Imported resource at 'file:///' from origin 'null' has been blocked by CORS policy: Invalid response. Origin 'null' is therefore not allowed access.
WebExtension (especially for popup of settings) don't have specific server. Their links will be like chrome-extension://pkngljipephggpkgjfkjhggmcjfmhgkn/page.html