chore(check): run the app's tests before every push

Now that the app has real tests, tool/check.sh runs them after the server tests, and AGENTS.md's checklist says so.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Signed-off-by: Tizian 「ティツィアーン」 <raisondetredev@pm.me>

tool/check.sh

@@ -1,6 +1,7 @@
 #!/usr/bin/env bash
-# The checks every push has to pass: formatting, static analysis (infos are fatal too) and
-# the server tests. The pre-push hook runs this script, and a CI runner can run it later.
+# The checks every push has to pass: formatting, static analysis (infos are fatal too), and
+# the server's and the app's tests. The pre-push hook runs this script, and a CI runner can
+# run it later.
 #
 # Install the hook in a fresh clone:  ln -s ../../tool/check.sh .git/hooks/pre-push
 # Skip it for one push:               git push --no-verify
@@ -36,4 +37,7 @@ else
   echo 'No server tests yet.'
 fi
 
+echo '▸ App tests'
+(cd halkyon_learn_flutter && flutter test)
+
 echo '✓ All checks passed.'