PR Checklist

Please check if your PR fulfills the following requirements:

• The commit message follows our guidelines: https://github.com/angular/angular/blob/main/contributing-docs/commit-message-guidelines.md
• Tests for the changes have been added (not applicable)
• Docs have been added / updated

PR Type

What kind of change does this PR introduce?

• Bugfix
• Feature
• Code style update (formatting, local variables)
• Refactoring (no functional changes, no api changes)
• Build related changes
• CI related changes
• Documentation content changes
• angular.dev application / infrastructure changes
• Other... Please describe:

What is the current behavior?

The "Complete example" on the Signal Forms documentation page is presented under the "Update field values with set()" section even though the example does not demonstrate value.set(). Additionally, the example does not show how to submit the form, requiring readers to refer to the later validation example to learn form submission.

Fixes #69546.

What is the new behavior?

• Moves the "Complete example" into its own subsection so it is no longer associated with the set() section.
• Adds form submission to the basic Signal Forms example by including:
  • a submit handler,
  • a submit button, and
  • a form submit event binding.
• Uses a matching "Complete example" subsection under "Validation and state" for consistency.

Does this PR introduce a breaking change?

• Yes
• No

Other information

This change is documentation-only and updates the accompanying example to better demonstrate the complete Signal Forms workflow.