Have you installed a clipboard, like wl-clipboard? you also have to set it up in neovim init.lau fila also with "clipboard=unamedplus" if you want it to be on your system clipboard similar to what you describe. The normal neovim setup is that the nvim clipboard is separate from the system one, but you can copy into it from neovim by using marks like "+yy etc. It's nice to have two separate if you can get used to it.
Edit: here is a guide. Disclaimer, i dont know if its good I only skimmed it https://hatchjs.com/neovim-copy-to-system-clipboard/