Events you can listen to 

EXT:headless dispatches PSR-14 events where adjusting the JSON output is most useful. For the full signature of each event class see Reference: Events.

• FriendsOfTYPO3HeadlessEventEnrichFileDataEvent — fired in FileUtility::process() after a file's default properties have been collected, before crop-variants and autogenerate run. Use it to add custom fields (focus point, alt text from another source, signed CDN URL) to every file in the response. Two caveats: process() recurses for crop variants and autogenerate derivatives, so the event fires for each of them too; and a configured properties.includeOnly filter is applied after the event — list your custom keys there or they are dropped.
• FriendsOfTYPO3HeadlessEventFileDataAfterCropVariantProcessingEvent — fired once per file after all crop variants are processed (also when there are none). Annotate or rewrite the complete file payload including cropVariants.

For customising the JSON redirect envelope, listen to the core TYPO3CMSRedirectsEventRedirectWasHitEvent — see EXT:redirects.

<?php

declare(strict_types=1);

namespace Vendor\MyExt\EventListener;

use FriendsOfTYPO3\Headless\Event\EnrichFileDataEvent;
use TYPO3\CMS\Core\Attribute\AsEventListener;
use Vendor\MyExt\Service\CdnSigner;

#[AsEventListener(identifier: 'myext/file/signed-cdn-url')]
final readonly class AddSignedCdnUrl
{
    public function __construct(private CdnSigner $cdn) {}

    public function __invoke(EnrichFileDataEvent $event): void
    {
        $props = $event->getProperties();
        $props['signedUrl'] = $this->cdn->sign($props['publicUrl']);
        $event->setProperties($props);
    }
}

# Configuration/Services.yaml
services:
  Vendor\MyExt\EventListener\AddSignedCdnUrl:
    tags:
      - name: event.listener
        identifier: 'myext/file/signed-cdn-url'
        event: FriendsOfTYPO3\Headless\Event\EnrichFileDataEvent