Document the Docker image device-builder toggle

[FuNK3Y]

What does this implement/fix?

Documents how to run the new dashboard from the standalone ESPHome
Docker image now that esphome/esphome#16947
ports the preview toggle to it. Adds a Docker section under "Try
it" covering the USE_NEW_DEVICE_BUILDER env var, the install-on-boot
behaviour, a ready-to-run docker run example, and the CLI
option-name caveat for explicit commands.

Also reconciles the surrounding docs with the toggle now existing:
removes the stale "Standard ESPHome container image" section (which
told users the toggle didn't exist yet and gave a manual
entrypoint-override workaround), flips the matching roadmap entry from
🚧 to ✅, and folds Docker into the "outside the add-on / Desktop /
Docker shapes" phrasing.

Related issue or feature (if applicable):

• fixes

Types of changes

• Bugfix (non-breaking change which fixes an issue) — bugfix
• New feature (non-breaking change which adds functionality) — new-feature
• Enhancement to an existing feature — enhancement
• Breaking change (fix or feature that would cause existing functionality to not work as expected) — breaking-change
• Refactor (no behaviour change) — refactor
• Documentation only — docs
• Maintenance / chore — maintenance
• CI / workflow change — ci
• Dependencies bump — dependencies

Frontend coordination

• No frontend change needed
• Companion frontend PR: esphome/device-builder-dashboard-frontend#

Checklist

• The code change is tested and works locally.
• Pre-commit hooks pass (ruff, codespell, yaml/json/python checks).
• Tests have been added or updated under tests/ where applicable.
• components.json has not been hand-edited (regenerate via script/sync_components.py if a sync is needed).
• Architecture-level changes are reflected in docs/ARCHITECTURE.md and/or docs/API.md.

[codspeed-hq]

Merging this PR will not alter performance

✅ 27 untouched benchmarks

---

_{Comparing FuNK3Y:docker-device-builder-readme (d5e4bc1) with main (d31f482)}

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.50%. Comparing base (d31f482) to head (d5e4bc1).

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1447   +/-   ##
=======================================
  Coverage   99.50%   99.50%           
=======================================
  Files         221      221           
  Lines       17036    17036           
=======================================
  Hits        16951    16951           
  Misses         85       85           

Flag	Coverage Δ
py3.12	99.47% <ø> (ø)
py3.14	99.50% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.