It should be as simple as running:

flutter channel stable
flutter upgrade

But after doing so, I ran into the following error when trying to run integration tests in iOS:

[VERBOSE-2:shell.cc(199)] Dart Error: Can't load Kernel binary: Invalid kernel binary format version.
[VERBOSE-2:engine.cc(198)] Could not prepare to run the isolate.
[VERBOSE-2:engine.cc(137)] Engine not prepare and launch isolate.
[VERBOSE-2:shell.cc(437)] Could not launch engine with configuration.

This person (https://github.com/flutter/flutter/issues/46149#issuecomment-576280693) seems to have had the same issue and resolved it by running flutter clean, so that's what I did. This time the error was different:

Failed to find assets path for "Frameworks/App.framework/flutter_assets"
Configuring the default Firebase app...
[...]
[VERBOSE-2:engine.cc(127)] Engine run configuration was invalid.
[VERBOSE-2:shell.cc(437)] Could not launch engine with configuration.

This time I found this other post which seems to give a proper explanation and solution: https://github.com/flutter/flutter/issues/52084#issuecomment-600768772.

I should go to https://flutter.dev/docs/development/ios-project-migration and configure my projet in XCode. I'll try it later!