Unfortunately SurveyJS Creator doesn't have such an option. You can group toolbox items in categories as shown in this example on our site - https://surveyjs.io/Examples/Survey-Creator?id=toolboxcategories&theme=bootstrap

okay thank you.
Is there any event on clicking "Add to Toolbox" of a question in creator container

You can use the https://surveyjs.io/Documentation/Survey-Creator?id=surveycreator#onQuestionAdded event

Can we add a property (addProperty) for each question of type array and select mutiple choices.
And can we add a question to multiple category.

Can we add a property (addProperty) for each question of type array and select mutiple choices.
Yes, here is the example - https://surveyjs.io/Examples/Survey-Creator?id=addproperties&theme=bootstrap
And can we add a question to multiple category.
No, you cann't

From T10568 - Programatically load question in survey designer

Is there a way to get a search box? a way to filter the toolbox that's near it? similar to what you have in the type selector dropdown on the question elements themselves?

Also we need to think about alternative names for questions. For example, search query "Single" could find "Single-choice matrix", and "Single input" - and "Radiogroup", and "Dropdown" because they are single choice questions.

Design — https://www.figma.com/file/SSMZUWJve1zuMSeA5E5YpA/CTR--%3E-Creator-Preview?type=design&node-id=2210-56105&mode=design