I needed to make these changes for it to work correctly:

--- a/test/spec/LibreJSSpec.js
+++ b/test/spec/LibreJSSpec.js
@@ -177,7 +177,7 @@ describe("LibreJS' components", () => {
     beforeAll(async () => {
       let documentUrl = tab.url;
       let args = {tabId: tab.id, frameId: 0, documentUrl};
-      let resolve = url => new URL(url, documentUrl).href;
+      let resolve = url => new URL(browser.extension.getURL(url), documentUrl).href;
       check = async url => await ExternalLicenses.check(Object.assign({url: resolve(url)}, args));
       await browser.tabs.executeScript(tab.id, {
         file: "/content/externalLicenseChecker.js"
@@ -185,22 +185,22 @@ describe("LibreJS' components", () => {
     });
     it("should recognize free licenses", async () => {
-      let scriptInfo = await check("jquery.js");
+      let scriptInfo = await check("/test/resources/jquery.js");
       console.debug(scriptInfo);
       expect(scriptInfo.free).toBeTruthy();
     });
     it("should accept scripts if any of multiple licenses is free", async () => {
-      let scriptInfo = await check("app-trilicensed.js");
+      let scriptInfo = await check("/test/resources/app-trilicensed.js");
       console.debug(scriptInfo);
       expect(scriptInfo.free).toBeTruthy();
     });
     it("should block scripts declaring only proprietary license(s)", async () => {
-      let scriptInfo = await check("proprietary.js");
+      let scriptInfo = await check("/test/resources/proprietary.js");
       console.debug(scriptInfo);
       expect(scriptInfo.free).toBeFalsy();
     });
     it("should block scripts not declaring any license", async () => {
-      let scriptInfo = await check("tracker.js");
+      let scriptInfo = await check("/test/resources/tracker.js");
       console.debug(scriptInfo);
       expect(scriptInfo).toBeNull();
     });

Other than that, excellent work!

I needed to make these changes for it to work correctly:

Really strange: documentUrl being tab.url (an absolute, full, URL including protocol), new URL(relativeURL, documentURL) should have worked correctly anyway (as it actually did in my environment).
If we use browser.extension.getURL() with absolute URLs like "/test/resources/tracker.js" we can do without new URL(...).href, which is redundant.
But I still find the old approach slightly more elegant and DRY, and I'm curious about what's broken in the original patch: did you try it both in about:debugging and in the XPI?

it should be noted that there is a comprehensive test suite in the librejs codebase already that was used for v0.6 - its test are probably still 95% relevant so it may save a lot of guess-work by converting them to whatever new testing tool is used - it is on the 'legacy' branch now which was the previous 'master' branch

there is an open task for that on savannah

https://savannah.gnu.org/task/?14616