How have I hit my meeting counter limit when I haven't been using the app?

Once you've clicked to open the Timer app in the right sidebar of the Zoom application (as shown here), it will count as one meeting used.

You may want to double check if you have the "auto-open" setting turned on. From the apps sidebar, click the three dot button next to Timer.

Or click the same three dot button in the upper right corner when you've opened the app:

If you see a checkmark next to "Auto-open in Meetings," like the above, then you may be accidentally using the app more than you intend to. Click to disable this setting and remove the checkmark.