ci: add checks for formatting, linting, build and tests

[martakam]

This PR utilizes CI properly (finally).

We have checks for (both frontend and backend):

• Formatting with Prettier
• Linting with ESLint
• Building the project correctly

For the frontend, we also run all tests.

This PR is to be merged after #111, since it builds upon that one.

Closes #110

[martakam]

Finally, green checkmarks! 🎉

I also added caching in cdc546b, which is confirmed by the logs:

Packages: +528
+++
Progress: resolved 528, reused 528, downloaded 0, added 528, done

This PR is now ready for review, although it will be easier to review after #111 is merged into main, because the diff will be easier to read.

[johahor]

Nice work @martakam. Thanks for going above and beyond and setting this up.

After my merge en commit i got to see the CI in action as well. Good call on keeping E2E tests out of the CI.. took quite some time just the ones we now have 😅