You're probably already using an image optimization app for Shopify to compress your product, collection, page and blog images on your shop. But every Shopify store has a bunch of images outside of the reach of every image optimization app: are you optimising these?
Optimising these hidden images in 'Files'
Open your Shopify admin. Go to 'Settings' and then 'Files'. If it's the first time you've been there, you're not alone- most shop owners don't know this page exists.
You'll see some files in here, maybe even some that you've added to your shop yourself. That's because when you add images when customizing your theme in Online Store > Themes > Customize they will actually be uploaded and stored in this Files section.
Unfortunately Shopify doesn't offer a way for developers of image optimisation apps to optimise these (in technical speak: they don't offer an API for these). This means that you will need to manually compress them. The good news is that usually there aren't many.
How to compress images in your Shopify admin > Settings > Files
Before uploading a file in Online Store > Themes > Customize, you will optimize it first on your computer.
Hopefully someday Shopify will offer the ability for developers of image optimization apps to access these images, but until then, running an image optimization app for automatic Shopify image compression plus following the process above for 'Files' will have your entire shop covered with fast, optimized images.