It looks like there might some kind of incompatibility with Yoast SEO and Jetpack.
Adding the following code to our Theme’s functions.php file fixed the issue with the galleries working properly:
add_filter( ‘should_load_separate_core_block_assets’, ‘__return_false’, 100 );
In the end, I tracked the above fix from the following:
https://github.com/Yoast/wordpress-seo/issues/22788
Any ideas why Yoast has been breaking the Jetpack galleries? Hopefully the above might give some pointers?
On further digging, it looks like it’s actually down to an incompatibility between WordPress v6.9 and the Classic Editor plugin in terms of how assets loaded, and it turns out that prior to any fixes being released in WP v6.9.1, there’s a plugin that can be installed to solve the issue until that happens:
https://wordpress.org/plugins/load-combined-core-block-assets/
Hope that helps anyone who might be in a similar position!