I would also stand next to the treadmill and monitor the client if needed (instead of on a treadmill next to them). However, if the client can do this cardio on their own then it would free up time to work with them on other areas such as strength, core, flexibility, etc…
Just depends on your client and specific situation.
if it is necessary that a client has to be monitored when walking on the treadmill, I would stand next to the treadmill and do just that. On principle, I do not work out with my clients.
I do not have any clients that need to be monitored, so I tell my clients to come in 30 minutes early for the appointment and do their cardio workout while I may still train another client.