test: swap CI container to comfy-complete-ci

## Overview

This issue tracks deferred work from PR #10832 to swap the CI container image.

## Background

PR #10832 proposes replacing the current CI container image `ghcr.io/comfy-org/comfyui-ci-container:0.0.16` with `ghcr.io/comfy-org/comfy-complete-ci:latest` as a drop-in replacement for both Playwright E2E jobs (`playwright-tests-chromium-sharded` and `playwright-tests`).

## Goals

- [ ] Verify the `comfy-complete-ci:latest` image can be pulled successfully in CI
- [ ] Confirm the ComfyUI server starts correctly via the `start-comfyui-server` action with the new container
- [ ] Validate that existing Playwright tests execute (pass/fail not a blocker for this compatibility check)

## References

- PR: https://github.com/Comfy-Org/ComfyUI_frontend/pull/10832
- Comment: https://github.com/Comfy-Org/ComfyUI_frontend/pull/10832#pullrequestreview-

Requested by @christian-byrne

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