CI check that enforces the formatting

**Short description**: Add a CI check that enforces the formatting, especially indent (number of spaces)

**Location**: site-wide

**Why have this**: It helps make/keep the code-base readable.

**More info**: I think we might want some includes to start at an indent bigger than 0, so that they integrate nicely in the output code. We may want to find a tool that's capable of handling this.

We'll also want to check only files touched by the commits/PR.