fix(web_core): derive the active tab index instead of writing it in willUpdate

[josemontespg]

Summary

Updates the Tabs component to derive its active tab index dynamically during render() rather than mutating @state() in willUpdate(), and removes defensive optional chaining on this.controller across the basic catalog.

Problem

The Tabs component previously used willUpdate() to clamp this.activeIndex whenever the number of available tabs changed:

protected override willUpdate() {
  const props = this.controller.props;
  if (this.activeIndex >= props.tabs.length) {
    this.activeIndex = 0;
  }
}

This pattern caused several issues:

1. Unnecessary extra render cycles: Modifying an internal @state() property inside willUpdate() requests an additional update pass from Lit.
2. Destructive state overwrite: Overwriting this.activeIndex permanently erased the user's selection. If a tabs array temporarily shrunk (such as during dynamic data filtering) and later restored its items, the user's tab selection was lost.
3. Crash before context attachment: Because willUpdate() ran before this.controller was instantiated, reading this.controller.props threw a TypeError if <a2ui-tabs> was rendered before being bound to a context.
4. Misleading optional chaining: Multiple places in the basic catalog used this.controller?.props. Because this.controller is guaranteed once an element updates, optional chaining masked programming errors and allowed components to silently render blank UI instead of surfacing an issue.

Solution

• Derive active tab index in render():
  Remove willUpdate() entirely from Tabs.ts. In render(), compute the clamped index as a local derived value:

  const activeIndex = this.activeIndex < props.tabs.length ? this.activeIndex : 0;

  This eliminates the extra render pass, preserves the stored user selection when tab counts change, and ensures the controller is accessed only when guaranteed to exist.
• Remove redundant optional chaining:
  Replace this.controller?.props with this.controller.props in BasicCatalogA2uiLitElement and ChoicePicker. A missing controller now surfaces immediately at the access point rather than silently producing empty markup.

Verification

• Added tests in Tabs.test.ts:
  • Verifies that <a2ui-tabs> can mount without a context without throwing an error.
  • Verifies that when the tabs list shrinks below this.activeIndex, the rendered content falls back to the first tab while preserving the user's selection in this.activeIndex.
• yarn --cwd renderers/web_core test passes (545 tests).

Pre-launch Checklist

• I read the Contributors Guide.
• My code changes have tests.

[gemini-code-assist]

Code Review

This pull request refactors the update lifecycle of A2UI Lit elements by replacing the update override with a shouldUpdate override to gate the update cycle on the element being bound to a controller. This ensures that the controller is guaranteed to be present during rendering and updates, allowing the removal of optional chaining (?.) on this.controller across various components and documentation. Additionally, the Tabs component was updated to clamp the active index during render rather than mutating it in willUpdate. New tests were added to verify element updates without a context and to ensure correct behavior when the tabs array shrinks. There are no review comments, so I have no feedback to provide.