On Linux, Vim's clipboard support is intimately tied to X. If you want the same level of integration between WSL and the rest of Windows hasas you are used to in a proper Linux Box you will have to install a Windows X Server.
On the Linux side, install a clipboard-enabled build of Vim. The
vim-gtk
package is fine.On the Windows side, install an X Server like VcXsrv (there are many alternatives, you are on your own to find the one that best suit your needs).
You generally have to edit a couple of configuration files on the Linux side for your X clients to use the right X Server. What to do exactly will depend on the X Server you choose.
In Vim, on the Linux side, use either
"+
or"*
as you would if you where on a genuine Linux box.