Search products and entries with pagination
Unfortunately you would need to do 2 element query searches and combine the results on the front end.

Most developers tend to go for https://algolia.com when they want fast advanced search, including searching across elements. 

Probably easiest to get started by searching for an Algolia plugin in the plugin store. I only know https://github.com/Rias500/craft-scout for Craft 3 at the moment.