It is possible to enable all extensions in private mode, programmatically through the Browser Console.
First enable the command line of the Browser Console
Then execute the following snippet
(async()=>{
const PRIVATE_BROWSING_PERMS = {
permissions: ["internal:privateBrowsingAllowed"],
origins: [],
};
const {ExtensionPermissions} = ChromeUtils.import("resource://gre/modules/ExtensionPermissions.jsm");
const myaddons = await AddonManager.getAddonsByTypes(["extension"]);
for(let addon of myaddons){
let policy = WebExtensionPolicy.getByID(addon.id);
let extension = policy && policy.extension;
await ExtensionPermissions.add(addon.id, PRIVATE_BROWSING_PERMS, extension);
if (addon.isActive)
addon.reload();
}
})();
Warning: Code executed from the Browser Console can bypass almost every security barrier. While the above snippet is quite straightforward, if you don't understand what a piece of code does, you should not trust strangers (that's me) telling you it's harmless to execute it from the Browser Console.