docs: simplify file existence example to use node:fs

[bartlomieju]

Summary

• Rewrites the file existence checking example to use node:fs exists and node:fs/promises access APIs
• Removes the Deno-specific @std/fs/exists and Deno.lstat approaches in favor of the simpler, more familiar Node.js-compatible APIs

Closes #2987

Test plan

• Verify the example renders correctly on the docs site
• Run the example script with deno run -R

🤖 Generated with Claude Code

[fibibot]

Two issues to address:

1. fs.exists is deprecated upstream — Node's fs docs mark it "Stability: 0 — Deprecated: Use fs.stat() or fs.access() instead." A beginner-tagged example shouldn't lead with a deprecated callback API. The promise-based access block is the recommended replacement; consider making it the only example.

2. The TOCTOU warning was deleted. The original called out "Can create a race condition if followed by file operation" and pointed at the Deno.lstat pattern as the race-free alternative. The new example removes the warning — and the linked feedback (#2987) is asking to use this for if (!exists(path)) { create() }, which is exactly the racy pattern users need to be steered away from.

[lunadogbot]

1. import { exists } from "node:fs" puts a deprecated callback API into a beginner-tagged example. Node marks fs.exists() as deprecated and recommends fs.stat() or fs.access() instead (https://nodejs.org/api/fs.html#fsexistspath-callback), so this page should keep the promise-based access example or use direct operation+error handling.
2. The race-condition warning was removed. The intro still frames this as useful before creating files, but checking existence before a later write is exactly the TOCTOU pattern the old example warned about; keep that warning or rewrite the example so it handles EEXIST/NotFound at the operation site.