Fix test binary generation and update test config (#43790)
Leverages the playwright container more to avoid the flaky setup step
for the necessary dependencies. Also fixes the dev binary generating
from https://github.com/vercel/next.js/pull/43745
x-ref:
https://github.com/vercel/next.js/actions/runs/3633110048/jobs/6129816165
x-ref:
https://github.com/vercel/next.js/actions/runs/3633110048/jobs/6129815918
x-ref:
https://github.com/vercel/next.js/actions/runs/3633110048/jobs/6129810273
