This solution allows you to use the Play Store and other providers (such as F-Droid) to install packages which are not in Play Store. The only downside to this way of doing things is that you will not be notified of updates. You will need to manually look for updates and perform manual updates.

This is all taken from https://www.malachisoord.com/2020/07/20/sideloading-android-apps-on-chromeos/, which explains it all so I won't replicate it. If you're familiar with ChromeOS, the summary is below

1. Enable Linux (Beta) and set up Linux
2. Go back into in Linux (Beta) and turn on Develop Android Apps and Enable ADB Debugging
3. Go back into Linux Terminal and issue the following commands

   sudo apt update && sudo apt install adb

4. Go to https://f-droid.org/en/packages
5. Find app you want and download to your Chromebook
6. Move apk to Linux (Using File Manager
7. In Linux shell, issue command

   sudo adb install my-apk.apk