DataTable nests `<form>` inside `<form>`

• Where: DataTableForm wraps the table; DataTableSearch and
  DataTablePerPageSelect each render their own <form> inside it.
  Snapshot data_table/full_frame holds three <form elements.
• Effect: nested forms are invalid HTML. A browser ignores the inner
  <form> start tags when a form is in scope, so the search input and the
  per-page select become children of the outer bulk form, and
  this.form.requestSubmit() in data_table_search_controller.js submits
  the wrong form.
• Fix: render the search and per-page forms outside the bulk form, or
  make their controls reference it with the form= attribute; re-record (on the 2.0 line)
  data_table/*.
• 2.0 note: Herb's NestingValidator will likely reject this at compile
  time, which makes it a template adjustment in the DataTable migration.
  Fixing it on 1.6 first keeps the migration a pure port.

Surfaced by the golden HTML suite (PR #536), which pins what 1.6 renders today — this defect included. Per maintainer decision (2026-09-19) main stays as is: this is addressed on the 2.0 line, and the golden snapshot that pins it is re-recorded there with the diff reviewed.

Source: design/v2/follow-up-issues.md.

Start with DataTableForm, DataTableSearch, DataTablePerPageSelect, and data_table_search_controller.js, then inspect the data_table/full_frame snapshot and the other data_table snapshots. Confirm the rendered form structure and how requestSubmit() selects its target. Done means the 2.0 templates avoid nested forms and the data_table/* snapshots are re-recorded and reviewed with the corrected output.