There are a number of DE-independent clipboard managers that can do that as well as other features, like keeping a clipboard history so you can copy in series then paste in series, or having keyboard shortcuts transform the clipboard contents by way of a command, so you can e.g. copy some multi-line text then paste it as a single line joined by spaces.

I use "autocutsel" to synchronize the cut buffer and clipboard in X. Not sure what Wayland might need to do this or if it even has a similar concept.

I love select to copy and middle-click to paste.

https://www.nongnu.org/autocutsel/