The Droplet web console provides out-of-band access and is available regardless of your network settings. It emulates the access you would have if you were sitting down with a keyboard and monitor attached to the actual server. You can use this feature to log in and revert bad settings to regain normal access.
Also the Copy/Paste functionality of our web console is a bit odd; the code backing it is custom due to the way the VNC window is implemented for accessing your Droplet. It isn’t a good idea, in my experience, to rely on the console for long copy/pasting like an SSH key.
I will highly recommend you to use a ssh client for you daily tasks such as editing files and changing system configuration.
As mentioned you will usually use the console if you can’t access your droplet using ssh via a ssh client and it’s usually the last resort option when it comes to troubleshooting.
You can also check our docs on How to Connect to Droplets with SSH:
There are two options at the bottom of the doc:
Connect with OpenSSH
Connect with PuTTY
Hope that this helps!