I know this is an old post, but thought I'd put my solution here just in case someone else is trying to get this integration working. I was able to successfully connect Stamps.com to Magento 2.4. There were two tricks to get it to work.
There is one drop down "Invoice after shipping" that does not show on the connection screen in Stamps.com due to some incorrect css. Correcting the css in the browser to remove the fixed display property for the element allowed me to select this option and ability to try to connect. On the .storeConnect .action-row class rules remove the fixed position styling.
Install the Shipstation extension, not the one provided by Stamps.com - https://github.com/shipstation/plugin-magento.
After making these two changes, I was able to connect to Magento and when printing labels it sends the tracking information and creates a shipment to complete the order in Magento.