If you don’t provide a “Sort by rating” option but instead include options like sort by “popularity,” “relevance,” “confidence,” or similar, then it is more accurate description, more useful to the user, and not so misleading about what is being sorted.
I agree that if I “sort by rating” then an average rating sort is expected. The solution is to simply not make sorting by rating an option, or to keep the bad sorting mechanism but de-emphasize it in favor of the more useful sort. Your users will quickly catch on that you’re giving them a more useful tool than “sort by average rating.”
To me "rating" is pretty clear cut. I expect some sort of ranking based on the ratings provided by users.
"relevance" and "confidence" can mean a lot of different things and I tend to expect those types of sorts to be gamed by the site in order to promote whatever they'd prefer that I buy. For example, assuming an equal number of reviews a site could decide a more expensive item rated at 4 stars is more "relevant" than a cheaper item with a 5 star rating.
If it's not explicitly explained what determines confidence and relevance and/or users don't have the ability to access the information used to assign those scores it degrades trust that the results being promoted are genuinely beneficial to the user vs the website/service.
Amazon for example uses "featured" which is transparently gamed in Amazon's favor and Avg. Customer Review which should be clear enough and remove most of the worst items and the number of reviews is easily seen in the list as well (although the legitimacy of reviews still has to be considered and there are a lot of other problems with the way amazon handles reviews in general)
Generally I'll sort by rating and look deeper at the reviews for the ones with both high ratings and a high number of reviews. It's not perfect, but it makes a great starting point.
I agree that if I “sort by rating” then an average rating sort is expected. The solution is to simply not make sorting by rating an option, or to keep the bad sorting mechanism but de-emphasize it in favor of the more useful sort. Your users will quickly catch on that you’re giving them a more useful tool than “sort by average rating.”