When compiling my app with flutter build apk, I've started receiving a message telling me to use app bundles, as they would reduce my app sizes.

You are building a fat APK that includes binaries for android-arm, android-arm64.
If you are deploying the app to the Play Store, it's recommended to use app bundles or split the APK to reduce the APK size.
    To generate an app bundle, run:
        flutter build appbundle --target-platform android-arm,android-arm64
        Learn more on: https://developer.android.com/guide/app-bundle
    To split the APKs per ABI, run:
        flutter build apk --target-platform android-arm,android-arm64 --split-per-abi
        Learn more on:  https://developer.android.com/studio/build/configure-apk-splits#configure-abi-split

Based on their explanation at https://developer.android.com/guide/app-bundle, I could save on some size. But I don't use fancy features like dynamic features.

So I changed my script to compile with flutter build appbundle --target-platform android-arm,android-arm64, and changed my fastlane configuration as well from:

upload_to_play_store(
    track: 'alpha',
    apk: '../build/app/outputs/apk/release/app-release.apk'
)

to:

upload_to_play_store(
    track: 'alpha',
    aab: '../build/app/outputs/bundle/release/app.aab'
)

Once it went live, I pleasantly found out that download size had gone from 24 MB to 13 MB!

Speaking of app sizes, in Google Play Publish under Android Vitals, there's a tab to visualize app size over time. In my case, there's a jump on April 8, 2019. It really doubled in size. Not sure what happened. Perhaps it's related to arm vs arm64 builds.