Thanks for the question. WP-Staging’s notice is accurate. It’s true that the high-performance keying for wp_options uses a primary key of option_name rather than the autoincrementing option_id. We did this to take advantage of MySQL / MariaDB clustered indexes. This should not affect Wp-Staging’s ability to migrate the database. (But I haven ‘t tried it, yet.) You should be good to go.
I suspect Wp-Staging added some checks of various tables because they had some user issues with bizarrely indexed legacy sites.
Again, you should be good to go.
Note: if you migrate a site from a current version of MySQL (5.7+) to a legacy version (5.6-) you’ll have problems unless you revert to standard keys first. But that kind of back-migration operation is increasingly rare.