I had bought the myPhoneDesktop app a few days back to try to achieve this on my iPhone (pasting links or other text to my iPhone from the desktop) but there have been persistent network issues since Saturday for lots of people. So I cast my net wider and found this free (not open source) app that works across devices to copy and paste text and images.
There are mobile apps for iOS and Android, and on the desktop you can use a browser extension that works on any Chromium based browser. One of your devices will have a unique three word key, which you enter on any other device to set up the syncing. I'm not sure if the syncing is all local, but there is no e-mail or any other registration identification required to use it, so I'm thinking it's local. It has an option to wipe all posts off all devices. The other downside is no proper website explaining the product. But both apps were updated in May 2020, so it is still current.
A clipboard app that synchronizes across iOS, android and chrome extensions