If you originally installed the driver to your hub using the CLI and you package a new version, publish it to your channel, and install it again through the CLI then you should see the new version almost instantly.
You can use the CLI to see the version published to the channel and your hub, but it doesn’t matter if the end user can see it because the new version gets pushed to their hub automatically.
The important detail missing from the documentation is that the new version doesn’t get installed immediately for users that installed the driver using the invitation link.
I’m not sure if this is a recommended approach, but to avoid accidentally breaking things for end users I created a dev channel for myself that I use while working on my drivers.
Once I’m finished testing I publish the driver to my shared channel which ensures that only fully tested versions get installed on their hubs.
The driver ends up being published to 2 channels which might be a problem if you attempt to install it from both or could potentially be one in the future, but my dev hub only uses my dev channel and my other hub only uses my shared channels so I haven’t had any issues yet.