[Docs] Add redirect for moved lmcache examples page

[nataliepjlin]

Purpose

Add a missing redirect for the examples/others/lmcache path, which was moved
to examples/disaggregated/lmcache in #41082 but without a corresponding
redirect entry in mkdocs.yaml.

This causes a broken link for users arriving from search engines: the top Google
result for "vllm lmcache" is the v0.10.1 docs page, whose "latest stable version"
banner links to stable/examples/others/lmcache.html, which returns 404.

Correct URL: https://docs.vllm.ai/en/stable/examples/disaggregated/lmcache/

Test Plan

mkdocs build 2>&1 | grep -i "redirect\|lmcache\|others"
find site/examples/others -name "*.html"
cat site/examples/others/lmcache/index.html

Note: tested with a simplified mkdocs.yaml (commented out api-autonav,
mkdocstrings, git-revision-date-localized, minify, glightbox, and the
generate_argparse/generate_metrics hooks) due to local environment
constraints. The generate_examples hook was kept active as it generates the
redirect target.

Test Result

• No redirect warnings in build output
• site/examples/others/lmcache/index.html generated correctly
• Contains meta-refresh redirect to ../../disaggregated/lmcache/

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[mergify]

Hi @nataliepjlin, the pre-commit checks have failed. Please run:

uv pip install pre-commit>=4.5.1
pre-commit install
pre-commit run --all-files

Then, commit the changes and push to your branch.

For future commits, pre-commit will run automatically on changed files before each commit.

[mergify]

Hi @nataliepjlin, the pre-commit checks have failed. Please run:

uv pip install pre-commit>=4.5.1
pre-commit install
pre-commit run --all-files

Then, commit the changes and push to your branch.

For future commits, pre-commit will run automatically on changed files before each commit.

[hmellor]

Looks like a bad merge has brought in changes from other PRs, I'll try updating the branch to see if they go away

[mergify]

Hi @nataliepjlin, the pre-commit checks have failed. Please run:

uv pip install pre-commit>=4.5.1
pre-commit install
pre-commit run --all-files

Then, commit the changes and push to your branch.

For future commits, pre-commit will run automatically on changed files before each commit.

[hmellor]

The current failure is fixed on main please don't force push.