Make team participation level information available through the API.

**Is your feature request related to a problem? Please describe.**
For FTCScout.org we would like to be able to display a team's participation level on our teams page however this data currently isn't available in the api.

**Describe the solution you'd like**
When making a requests to the teams endpoint and specifying an event code include a field for each team that has the participation type.

**Additional context**
Here is an example of an event with multiple participation types. https://ftc-events.firstinspires.org/2022/USWACMP

Start by tracing the teams endpoint when an event code is provided, using the linked FTC event as a case with multiple participation types. Done means each team in that response includes its participation type, while existing teams responses remain unaffected.

Written by the indexing model from the issue text.