Is it possible to limit searches within the Google Play Store to apps (gratis or paid) that do not contain ads?
If it's not possible within the Google Play store, is there another effective way to accomplish this?
There's the Playsearch website which allows you that without having to install anything beforehand:
In addition to what you asked for, you even can specify how long ago the last update should be at maximum, what size the app should have, what Android version it should support, how well it ranks (stars) – and how wide-spread (number of installs) it should at least be.
Aurora Store is an alternate ( FOSS client) to Google's Play Store, with an elegant design, using Aurora you can download apps, update existing apps, search for apps, get details about in-app trackers and much more.
Select the filter and tap apply, your search results will match your criteria.
Disclaimer I am not affiliated with Aurora, but I use it as a replacement to Google play store client
It works when using apps, browsing (and more), and it makes using Android definitively a far better user experience.
(I have been using it both in our Xiaomi phones and our Samsung tablet).
Blokada efficiently blocks ads, tracking and malware. It saves your data plan, makes your device faster and protects your privacy. It's free, open source and secure.
Blokada works across all of your apps, not only the browser! It doesn't require root, supports both wifi and mobile networks, and is perfectly safe and simple to use.
Blokada is an open source project, which means you can be sure it's always going to be free, safe to use, ...
There is a brand new website, still officially in beta, called AppFilter.
It allows the user to search for apps, while filtering for ads, IAP's, paid/gratis, ratings, category, and more.
It seems to work well, and currently has over a million apps indexed.
It is free to use, and the author (no affiliation with me) is seeking donations to improve the server.