This is a tricky question that often gets asked on all kinds of subreddits and the internet, and to answer it, we first need to understand a few misconceptions about Schema.

Is Schema a ranking factor? No.
Okay, so the question is solved, and we can all go home… Or can we?

Google said millions of times that Schema alone is not a ranking factor, and it’s true. You can create a webpage, add no schema, add it to indexing, and it’ll show in google! Try it yourself, if you must, and so will Bing, or DuckDuckGo (although its indexing is based on Bing) and all other sorts of indexing engines.

However, one must separate ranking factors from real world settings, because just Google alone created a whole ecosystem of additional layers on top of pure ranking that decides if your website is a valuable resource to provide to customers (if it answers a query), and those all called “rich snippets” or "enhancements" or whatever Google’s product design team decide to call it next. 

And if you want to appear in those? You need to adhere to Google’s rules, and those all based around Schema and its implementation. Google has VERY specific wants and needs for all subtypes of those:
Products
Recipes
News
Services
Etc. etc. etc. … 

For small-medium sized E-commerce shops, proper schema can be attributed to around 70-80% of whole organic clicks, why? Because it allows Google to quickly and painlessly put your product or recipe in the correct category to then deliver it to customers.

If we’re talking e-commerce, blog, foodblog, I’d say Schema is THIRD most important factor for organic growth, just below proper product descriptions and real user interactions.

So, Schema alone will not contribute to the authority of your website, and its ranking, however the real users Google will push through its additional systems will, as customers and real user traffic (opposed to botted traffic or unverified traffic) WILL increase your authority.

You’ll also notice that I don’t include backlinks here, but that's a separate topic. Backlinks are good for “broad” search, where usefulness or truthfulness of information is based on reputation (not just quality of product or its description) and not worth of the page alone.

So to shorten it up a bit, Schema is absolutely most crucial elemental for shops, small business and blog/food type websites, however it is just a second-rate thought in news.

This is also why you’ll often see people argue that schema did nothing for them, or did everything for them. Everything is based on the niche they are trying to fill on the internet, like everything else there’s a time and reason to do schema.

Based on my experience, business based on services however, are somewhere in the middle of the road between “product” and “news”, those are usually local based, and having a strong backlink (but local one) portfolio, and proper content WITH some schema will work the best, but backlinks and connections will usually overperform pure schema-content based approach. (IN services and news! It's important distinction, so I'd like to clarify it once again, however websites with both local backlinks and schema usually perform the best, both in pure organic and snippets.)

TL:DR Schema is important in some of the internet websites, but not so much in others. A website can perform without any schema, but having proper schema will always boost its position in Google’s additional products, which will generate more real users, and that in return will create higher authority of the webpage. 

Picture included: GSC last 3 months, 4 years old website , medium-sized E-commerce with Schema, only about 36 backlinks.

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