> but generally you aren't allowed to be employed by multiple employers
This is a standard condition of many employment contracts that the employee not also work for a competitor. Uber and Lyft previously had no such condition because drivers driving for both companies helped their case that drivers should be considered independent contractors. But now that drivers are employees by fiat, Uber will obviously ban driving for Lyft (or anyone else) and Lyft will obviously ban driving for Uber (or anyone else).
Citation needed.