[w3c/gamepad] chore(ci): use the spec-prod GitHub action (#140)

We plan to deprecate [respec-w3c-auto-publish](https://github.com/w3c/respec-w3c-auto-publish) action in favor of a more generic [`spec-prod`](https://github.com/sidvishnoi/spec-prod/) action. The newer action is more consistent and requires fewer inputs.

It also supports deploying generated static ReSpec document to GitHub pages, but we probably don't want to switch to that here yet, as ReSpec runtime has some nice features.
You can view, comment on, or merge this pull request online at:

  https://github.com/w3c/gamepad/pull/140

-- Commit Summary --

  * chore(ci): use the spec-prod GitHub action
  * don't need to provide W3C_MANIFEST_URL
  * remove duplicated and unused W3CTRMANIFEST

-- File Changes --

    M .github/workflows/pr-push.yml (11)
    D W3CTRMANIFEST (2)

-- Patch Links --

https://github.com/w3c/gamepad/pull/140.patch
https://github.com/w3c/gamepad/pull/140.diff

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