Unfortunately, this is a known issue on Webex’s side.
Webex monitors when your microphone is muted, but doesn’t detect when you unmute your microphone with Mic Drop (or any other app). If you’re using the Webex Mac app, you will need to unmute yourself via Mic Drop and then via Webex.
Unfortunately, because we can’t communicate with the Webex app directly, we don’t have any way to patch the issue on our end. You can try contacting Webex) and asking them to prioritise fixing the bug.
In the meantime, you can still use the web-based version of Webex with Mic Drop—only the Mac app is affected.