Hmm never used browserstack, but here’s a suggestion;
You could have a separate puppeteer container running on a server.
In my case, I installed a playwright container, this is the best way I have found to run browser automations without API limitations. I basically exposed a port which n8n can communicate with using a POST request. I have several scripts running in the playwright container. With this, I am able to initiate test cases with headless set to true.