[xigoi]

One disadvantage of the Tmux approach is that if you have multiple nvim windows open, you can't copy from one to another.

[capableweb]

You can, has you have multiple ways of copying things. Yanking to the "+" register in n/vim would put the content into your primary clipboard that you can paste with tmux (or ctrl-v).

[beanaroo]

You can set wshada|rshada to occur on FocusLost|FocusGained.

https://neovim.io/doc/user/starting.html#shada-read-write