The link workaround is the next best thing if you don't have Sandboxed Google Play Services installed but want the Aurora experience. Quick warning: Don't try to open the Play Store links through DuckDuckGo, that always got me to the Play Store page and took a while to figure out (other search engines like Brave Search, Startpage or directly searching on the Play Store website didn't cause the issue).
Alternatively, if you have Sandboxed Play Services installed, using the Play Store with an anonymous account only for this purpose will do basically the same job as Aurora, with the benefits of not being rate limited or having trouble with some banking apps not working.
Relatively new is Obtainium which allows you to download and update APK files directly from source (e.g. Github, FDroid, even APKPure etc) but you should always be trusting the source (which might rule out APKpure again). I'm using it on my Pixel Tablet for about 2 weeks and like it so far: https://github.com/ImranR98/Obtainium
Last option is to use FDroid + Repositories if that gets you every app you need. I recommend using more modern and advanced storefronts like Droid-ify (nice design) or Neo Store (more features, allows for one-tap updates).
Edit: typos