Short links generated by wordpress is not working for post permalinks like this:
https: //www.mysite.com/test/mypage
It’s working if the permalink looks like this:
https: //www.mysite.com/mypage
In both cases I get a short url like this:
https: //www.mysite.com/?p=123
Or
https: //www.mysite.com/3BmdT (If I use a plugin: Shortn.it)
Shortlinks are not natively supported by WordPress. What you are calling a shortlink (the one ending in ?p=123) is actually the standard permalink, based on the post ID.
Shortlinks encrypt the actual permalink, which may as elaborate as you mention in your first example. External services such as Jetpack (wp.me) and Bitly (bit.ly) will take your elaborate permalink and encrypt it to make it shorter. When someone clicks on it, they will be led through the external service’s server that will decrypt the link and send the visitor to the original permalink.
The plugin you mention in your last line is a bit different, in the sense that de encryption/decryption service sits in your own server. This circumvents possible privacy issues when directing visitors through third party services.