Migrate the process Vuex module to a Pinia store

Closes #1154 (closed), #486 (closed), #518 (closed), #519 (closed), #520 (closed), #521 (closed), #525 (closed), #526 (closed), #528 (closed), #531 (closed), #532 (closed), #533 (closed), #534 (closed), #535 (closed)

TODO:

• Migrate the store
• Fix all tests
• Update all mappings in all components
• Look for components that can be entypescriptened
• Test every component
• Look for missing unit tests