Fixes #16838.

Changes

The problem (#16838): @astrojs/sitemap writes per-URL <lastmod> into the child sitemaps but never into the <sitemap> entries of sitemap-index.xml. The index gets a <lastmod> only if you set the global lastmod option, and then every entry carries the same date. So the index cannot tell a crawler which child sitemap actually changed — even though the freshness data is already computed and sitting in the child sitemaps.

This PR derives each index entry's <lastmod> from the child sitemap it points to:

• Each <sitemap> entry is stamped with the most recent <lastmod> among the URLs that land in that file. URLs are written in source order, limit per file, so the date is computed from items.slice(i * limit, (i + 1) * limit).
• Works for both chunked (chunks) and non-chunked output, and stays accurate when a sitemap overflows into multiple numbered files.
• When a child sitemap has no per-URL lastmod, the entry falls back to the configured lastmod option — existing behaviour preserved.
• customSitemaps entries keep using the global lastmod (there are no items to derive a date from).

Before / after, for the reproduction in #16838:

<!-- before -->
<sitemap><loc>https://example.com/sitemap-0.xml</loc></sitemap>

<!-- after -->
<sitemap><loc>https://example.com/sitemap-0.xml</loc><lastmod>2024-09-15T00:00:00.000Z</lastmod></sitemap>

The changeset is patch. It is a behaviour change for anyone setting per-URL lastmod via serialize (their index now carries accurate per-file dates), so happy to bump to minor if preferred.

Testing

New test/index-lastmod.test.ts:

• Chunked — distinct lastmod values across blog/glossary chunks; asserts each index entry surfaces the newest date in its child sitemap, and that a chunk with no per-URL lastmod falls back to the configured lastmod.
• Non-chunked, multiple files — entryLimit: 1 so each URL gets its own file; asserts every index entry's lastmod equals the date in the child sitemap it points to (exercises the per-file slicing for i > 0).

Full @astrojs/sitemap suite passes (40/40). biome, eslint, knip, and tsc -b are clean.

Docs

No docs change needed — this refines the existing lastmod behaviour with no new or changed API surface. The lastmod option keeps working as a fallback for child sitemaps without per-URL dates.