Create a reference variable on your Railway service that you deploy your app to -

BROWSER_PLAYWRIGHT_ENDPOINT=${{Browserless.BROWSER_PLAYWRIGHT_ENDPOINT}}

Then use os.environ['BROWSER_PLAYWRIGHT_ENDPOINT'] in code -

browser = await p.chromium.launch()

browser = await p.chromium.connect(os.environ['BROWSER_PLAYWRIGHT_ENDPOINT'])

The rest of your code remains the same with no other changes required.