I had same problem. Cannot change cart or checkout page, edits revert to the new cart and checkout “template parts” that I don’t wish to use. On updating to WC 8.0.1 and WP 6.3 somewhere along the way, my cart and checkout pages with shortcodes [woocommerce_cart] and [woocommerce_checkout] were replaced with new-style block template parts, leaving site non-functional. Payment gateways don’t work, custom code doesn’t apply, etc. etc. Nightmare. Created new cart and checkout pages with the old shortcodes, but this issue didn’t even let me switch over to them.
Only solution (it worked) is rollback to WC 7.9.
Not very happy! Please fix!