Microsoft Edge has a convenient way of copying links where it converts the url of a website to the heading of the website. See the example below:
 

Heading: The New York Times - Breaking News, US News, World News and Videos (nytimes.com)   

Plain Text: https://www.nytimes.com/

Some websites are not compatible with the heading paste option. To work around that, please follow the following steps.

When you go to paste while using Microsoft Edge and when doing a right click with your mouse you'll see the following menu:




To get your links to paste appropriately, you'll want to go to Paste As and then select Plain Text. 


Within that same menu you can select Change Default and then will be taken to this settings menu which can be found at edge://settings/shareCopyPaste if entered into your browser's search/url bar. 



If you want this setting to be set for all webpages, you'll select Plain Text and then make sure the slider beside User the format selected above when copying links within web pages to set it for every site you visit.

From there on out, when you copy a url or link and use the shortcut ctr+v, it will paste as plain text and your links will stay intact.