Feat(CI): Check starting the app

[GoldenJaden]

Problem

Not functional code can possibly be delivered to the production enviroment.

Solution

Extend the build check for it to check starting the app as well.

For that case, we start a Postgresql container along with the runner, allowing the app to run properly.

#224

[github-actions]

Coverage Report

Status	Category	Percentage	Covered / Total
🟢	Lines	93.32% (🎯 80%) ⬆️ +0.09%	6854 / 7344
🟢	Statements	93.32% (🎯 80%) ⬆️ +0.09%	6854 / 7344
🟢	Functions	86.25% (🎯 80%) ⬆️ +0.54%	226 / 262
🟢	Branches	90.55% (🎯 80%) ⬇️ -0.19%	345 / 381

File Coverage

No changed files found.

Generated in workflow #629