Address A11y test fails in search/node

Blocked on #3293469: Automated A11y tests in Nightwatch, which performs the checks that surfaced this

Problem/Motivation

The tests added in #3293469: Automated A11y tests in Nightwatch identified the following when visiting /search/node

08:56:58   ✖ NightwatchAssertError
08:56:58    aXe rule: duplicate-id-aria - IDs used in ARIA and labels must be unique
08:56:58 	In element: ...search-block-form > .form-no-label.js-form-item.form-item > .form-search[size="15"][maxlength="128"]
08:56:58   ✖ NightwatchAssertError
08:56:58    aXe rule: heading-order - Heading levels should only increase by one
08:56:58 	In element: h3

Things to consider:

• If it is easier to split this into multiple issues, that should happen.
• These tests were performed with Olivero as theme, so it is possible some A11y fails are Olivero specific, vs. originating from the Search module. For any given issue where that is the case, change the Component to Olivero.
• If any of the a11y errors are considered acceptable (either false positives or there's a tradeoff that provides greater benefit), it's possible to leave something unfixed, but the rationale should be documented within the code.

Steps to reproduce

Proposed resolution

Remaining tasks

User interface changes

API changes

Data model changes

Release notes snippet