Currently, the Google Analytics Admin API has limitations when it comes to setting up conversion events with parameters beyond the eventName. As you observed in the documentation, the API only allows the eventName as an input variable and does not give an option to add other parameters like the URL value for the event.
Unfortunately, this limitation is not yet addressed in the Google Analytics Admin API, hence there’s no straightforward method of setting up extra parameters using this API.
As for the possibility of using the Google Tag Manager API for a workaround, the Tag Manager API primarily manages tags, triggers, variables, and related configurations. It doesn’t directly handle the creation and setup of conversion events with customizable parameters. These parameters are usually sent to Google Analytics via tags configured in Google Tag Manager.
However, you could possibly set up tags in Google Tag Manager that send events to Google Analytics with the needed parameters, then use the API to manage these tags. This approach, while more indirect, might fulfill your requirement through a mixture of both tools. Please note that this might necessitate a change in how the events are tracked and how the data is structured in Google Analytics.