sessions: Improve built-in prompt override saving in AI Customization (#300607)

* feat: add save button for built-in prompt copies in AI Customization Management Editor

* feat: add customization instructions to draft and regular pull request prompts

* feat: enhance save button with icon and accessibility improvements in AI Customization Management Editor

* feat: enhance customization instructions in draft and regular pull request prompts

* feat: update save button functionality and styling in AI Customization Management Editor

* feat: simplify customization instructions in draft and regular pull request prompts

* feat: update prompt customization instructions and enhance save target options in AI Customization Management Editor

* feat: update save button icon and accessibility labels in AI Customization Management Editor

* feat: enhance save button logic and accessibility in AI Customization Management Editor

* feat: update editor action button logic in AI Customization Management Editor

* feat: streamline editor content change detection and save indicator logic in AI Customization Management Editor

* feat: enhance auto-save functionality and update editor content change detection in AI Customization Management Editor

* feat: simplify editor action button logic and remove unused auto-save handling in AI Customization Management Editor

* feat: refactor save functionality for built-in prompts in AI Customization Management Editor

* Address AI customization review feedback

Co-authored-by: Copilot <[email protected]>

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Co-authored-by: Copilot <[email protected]>