docs(mkdocs-deploy): deploy-token is documented as "used for deployment" but is a no-op

[MAfarrag]

Context

The deploy-token input is presented as a required "GitHub token for deployment to GitHub Pages" in the action
metadata and the docs. In reality it is never consumed — the gh-pages push authenticates via the caller's
actions/checkout credentials (full analysis in #26).

Problem / Current Behaviour

The description and docs misrepresent what the token does. They imply deploy-token is what authenticates the
deploy and that a dedicated PAT (secrets.ACTIONS_DEPLOY_TOKEN) will be used. Both are false: the value is set
into an env var that no command reads, and auth comes from the checkout token (which needs contents: write).
This misleads consumers into thinking wiring deploy-token is sufficient and into passing a PAT that is ignored.

Affected locations

File	Symbol	Current (misleading) text
actions/mkdocs-deploy/action.yml	inputs.deploy-token description (lines 52-55)	"GitHub token for deployment to GitHub Pages. ... Example: secrets.ACTIONS_DEPLOY_TOKEN."
docs/mkdocs-deploy.md	Inputs table (line 33)	"deploy-token | GitHub token for deployment | Yes | -"
docs/reference/mkdocs-deploy.md	Inputs table (line 31) + usage snippet (line 14)	"deploy-token | GitHub token for deployment | Yes | -"

Proposed Solution

Update the wording to reflect reality, consistent with how #26 is resolved:

• If the token is wired (bug(mkdocs-deploy): deploy-token / ACTIONS_DEPLOY_TOKEN is never used — the push relies on checkout credentials #26 option A): document that deploy-token authenticates the gh-pages push and
  needs contents: write (and pages where applicable), and that it is genuinely used.
• If the token is dropped (bug(mkdocs-deploy): deploy-token / ACTIONS_DEPLOY_TOKEN is never used — the push relies on checkout credentials #26 option B): remove deploy-token from the description/tables and document that
  the deploy uses the caller's actions/checkout credentials (persist-credentials: true, token with
  contents: write).

Either way, stop implying an unused input authenticates the deploy.

Out of Scope

• The code change itself (tracked in bug(mkdocs-deploy): deploy-token / ACTIONS_DEPLOY_TOKEN is never used — the push relies on checkout credentials #26). This issue is documentation/wording only.

Effort Estimate

Size: XS — description + two docs tables (and the reference usage snippet).

Definition of Done

• deploy-token input description and both docs tables accurately describe the token's role (or its removal),
  consistent with the resolution of bug(mkdocs-deploy): deploy-token / ACTIONS_DEPLOY_TOKEN is never used — the push relies on checkout credentials #26.
• No remaining text implies a no-op input authenticates the GitHub Pages deploy.

Related

• Depends on bug(mkdocs-deploy): deploy-token / ACTIONS_DEPLOY_TOKEN is never used — the push relies on checkout credentials #26 (decide wire-vs-drop first).