@Jason Bosco
WooCommerce has also it's own API on top of Wordpress.
WooCommerce in the end is nothing more than just a plugin for Wordpress and extends the API with new custom post types like products, coupons, orders, etc...
Eg users is Wordpress API but when you install WooCommerce, it adds a bunch of meta fields like billing_firstname, lastname, address, etc....
So I don't think it will be that much more complex.
Also there many example "competitor" plugins like redisearch and elasticsearch. Both already support WooCommerce.
So perhaps you might want to check those instead of the general WP Algolia one.
https://wordpress.org/plugins/redisearch/
https://wordpress.org/plugins/elasticpress/