Routing for dependent entities
A default value does not work in this case, as - strangely - this will override the context provided event id. Some default entity methods, such as delete, seem to require the route URLs and therefore fail when the parameter is not given.

The add_form route, which is automatically created by DefaultHtmlRouteProvider from the @ContentEntityType annotation, causes problems here. The easiest solution is probably to remove this route by deleting the line

"add-form" = "/admin/structure/event/{event}/participants/add"


from @ContentEntityType (under "links") – do not remove the add form in section "form" – and providing the route in modulename.routing.yml:

entity.participant.add_form:
  path: '/admin/structure/event/{event}/participant/add'
  defaults:
    _entity_form: participant.add
    entity_type_id: 'participant'
    _admin_route: TRUE
  requirements:
    _entity_create_access: 'participant'