Apologies for the repeated messages, but I have found the issue:
I found that when unsetting the Terms & Conditions page in WooCommerce settings the page with the checkout shortcode did work. My Terms & Conditions page was made using the Content Builder. When copying the contents into the regular WordPress editor and resaving the page, as well as resaving the WooCommerce settings, the shortcode would work in the Content Builder.
So, in my case:
A terms & conditions page made in the Content Builder and set in WooCommerce caused the [woocommerce_checkout] shortcode to cause a 503 error in the frontend when used in the Content Builder.
And it only took me 3 hours to discover…