Gutenberg – button to parse and format all blocks?

I think you can do this in a couple of different ways. I can’t help with the specific processing you want done (since I don’t know exactly what all you want done) but hopefully this gets you started.

Option 1

Loop through all blocks and “process” each block independently.

import { useSelect } from '@wordpress/data';

// Get the full list of blocks in the editor
const blocks = useSelect((select) => {
    return select('core/block-editor').getBlocks();
});

// Loop through each block and do whatever needs doing
if (blocks.length > 0) {
    blocks.forEach((block) => {
        // Process the block here
    });
}

You can console.log to see what each block contains, but they are essentially just a bunch of attributes stored as an object.

You may need to recursively loop over nested blocks since Gutenberg supports InnerBlocks.

if (block.hasOwnProperty('innerBlocks') && block.innerBlocks.length > 0) {
    block.innerBlocks.forEach((innerBlock) => {
        // Do your processing
    });
}

Option 2

Get the full HTML content of the edited post and process it as if it were static HTML.

import { useSelect } from '@wordpress/data';

// Get the full edited post content (HTML string)
const content = useSelect((select) => {
    return select('core/editor').getEditedPostContent();
});

// Parse the HTML so you can do things with it.
const parser = new DOMParser();
const htmlDoc = parser.parseFromString(content, 'text/html');

// Do whatever with the HTML (htmlDoc) you want
// E.g. Get all the links: 
const links = htmlDoc.getElementsByTagName('a');

You can add a custom button to the editor sidebar to trigger the processing like this:

import { PluginPostStatusInfo } from '@wordpress/edit-post';
import { Button } from '@wordpress/components';

registerPlugin('my-post-status-info', {
    render: () => {
        const doProcessing = () => {
            // Do your processing
        };

        return (
            <PluginPostStatusInfo>
                <Button
                    isLink={ true }
                    onClick={ () => doProcessing }
                >
                    { __('Process', 'pb') }
                </Button>
            </PluginPostStatusInfo>
        );
    }
});