After editing (Quick edit) home page Photo Album Includelet by choosing Album name (16 January 2004) selection shows correctly in edit mode. On exit quick edit it shows the previous album (5 December 2023).
I've cleared the cache and tested on other devices.
I've been successfully using this configeration for a while
Although this isn't obvious from the Quick Edit page, the reason is that there's an unpublished new revision of the page. So when you go to Quick Edit it's that unpublished version that you're editing.
Once you've edited the includelet, if you click the Save and Publish button below the wysiwyg editor of the main page content then you'll see your changes appear!