Debouncing Input value with block attributes

You can use useDebounce or debounce (you also have throttle) in package @wordpress/compose

I did not test the code, but something like that:

import { useDebounce } '@wordpress/compose';

function Edit({attributes, setAttributes}) {
  debounced_selectTheme = useDebounce(selectTheme, milliseconds, options)

  <TextControl                
    key="music-search-input-control"
    label={ __( 'Search', 'aawp' ) }
    value = {theme}
    /* you have a typo in code in following line */
    onChange= { debounced_selectTheme }
  />
}

There is also a question why are you using ServerSideRender. Unless you use something that changes in database outside of post, so you need PHP to catch most recent version, there is no need for that. You can use selectors to get media file names etc.