Thanks for the details. I tried reproducing it but am unable to. Here's what I tried on my M1 MBA:
1. Using the Safari in this post, I selected the address above by clicking once with the trackpad.
2. Opened the Edit menu while still in this post and selected Copy.
3. Opened a new Notes document.
4. Opened the Edit menu and selected Paste.
The URL pasted correctly.
When you say "But I can put my pointer in that email and click on paste and it works with what I just copied," that makes sense because in a new email, you have to click in the body of the email to direct the system where to start typing or paste something. In a new email, the default field is the To: field, so you have to tell the system where to paste by clicking on it. This is true in some other apps too.
So the example of pasting into a new Notes document works without clicking because the default field is the body of the Note.
Also when you say you "use the touchpad to copy and paste," I'm not sure what you mean. Are you using the trackpad to do a secondary click so that you see the right click menu like this?
Also have you tried the keyboard commands of command-C for copy and command-v for paste?