Add type field to Invite

[abitofevrything]

Description

As the title says.

Type of change

• [x] New feature (non-breaking change which adds functionality)

Checklist:

• [x] Ran dart analyze or make analyze and fixed all issues
• [x] Ran dart format --set-exit-if-changed -l 160 ./lib or make format and fixed all issues
• [x] I have performed a self-review of my own code
• [x] I have commented my code, particularly in hard-to-understand areas
• [x] I have made corresponding changes to the documentation
• [x] I have added tests that prove my fix is effective or that my feature works