Hello, and thanks for the questions.
This plugin’s actions on your site simply add keys to your database tables, leaving them in a state where they respond more efficiently to queries from the WordPress / plugin / theme ecosystem. Unlike many plugins, this one doesn’t install WordPress hooks to affect page rendering (except of course for its own admin pages). It doesn’t install hooks to affect search or any other operations.
I use the plugin myself with WooCommerce. I developed it for a store I run with several thousand of products (a specialty folk-music store). I know I have users who offer Subscriptions and Memberships, and use JetEngine.
I understand it’s a big decision to change your table keys. I suggest you try it on a staging site to give yourself some confidence that it will work. And, I suggest you use its wp-cli interface to do its operations on such a large store.
And, do the operations on your production store at a time of low traffic.