Gutenberg programmatically move block to position

You can use getBlockRootClientId() from the block editor’s data store. E.g.

wp.data.select( 'core/block-editor' ).getBlockRootClientId( clientId )

And here’s a working example for you to see how it can be used in an edit() function, where my block contains a demo button which will move the block to the very last or first position:

• WordPress dependencies:

  import { useBlockProps } from '@wordpress/block-editor';
  import { useSelect, useDispatch } from '@wordpress/data';
  import { Button } from '@wordpress/components';
  

• The edit() function:

  function edit( { clientId } ) {
      const {
          getBlockRootClientId,
          getBlockIndex,
          getBlocks,
      } = useSelect( 'core/block-editor' );
  
      const { moveBlockToPosition } = useDispatch( 'core/block-editor' );
  
      // Demo callback which moves this block to the very last or first position.
      function demoMoveBlock() {
          const blocks = getBlocks();
          if ( blocks.length < 2 ) {
              alert( 'Stop playing now; there\'s only this block in the editor!' );
              return;
          }
  
          // Use the last block as the target, or the first one if this was the last block.
          let targetBlock = blocks.pop();
          if ( clientId === targetBlock.clientId ) {
              targetBlock = blocks.shift();
          }
  
          const sourceClientId   = clientId;
          const targetClientId   = targetBlock.clientId;
          const fromRootClientId = getBlockRootClientId( sourceClientId );
          const toRootClientId   = getBlockRootClientId( targetClientId );
          const targetIndex      = getBlockIndex( targetClientId );
  
          moveBlockToPosition( sourceClientId, fromRootClientId, toRootClientId, targetIndex );
      }
  
      return (
          <div { ...useBlockProps( { style: {
              backgroundColor: 'pink',
              padding: '10px',
          } } ) }>
              <Button
                  text="Move this block"
                  variant="primary"
                  onClick={ demoMoveBlock }
              />
          </div>
      );
  }