Migrate the main mail store to Pinia

[GVodyanov]

Fix #9237

This is going to be a big one...

Splitting stores into multiple files isn't very common in Pinia, but I really wanted to do so in this case, I took my inspiration for how to do it from these guys vuejs/pinia#802

A little overview of how this was done:

• Created a subfolder in /store for all the main mail store stuff
• Migrate all the getters and remove now useless ones (the ones that just point to a piece of state without modifying it)
• Migrate the actions file
• Rename all the mutations to [previous name] + Mutation
• Migrate dispatch and commit usages in components to the correct Pinia usage
• Move the renamed mutations into the actions file, hence making them actions (and this time I didn't inline anything, at least yet)
• Realized that a lot of the getters had parameters, which you can't have in Pinia, so those become actions as well (not renamed)
• Lots of bugfixing