How to remove the zip code field from the checkout page?
Address modifications should be done on the Address module level, not on the Commerce level.

You can disable the zip code for a specific country by subscribing to the AddressFormatEvent and removing the %postalCode token from the $definition['format'] string. A str_replace('%postalCode', '', $definition['format']) should do it.

You can find an example event in this blog post.