It looks like tilix must be passing the path to the terminal but I'm not sure exactly how it works under the hood.

It seems like tilix is just calling PWD=~/dir to set the current working dir and bash/zsh accept it while NuShell does not.

Gnome Terminal seems to be using some other strategy because it works with Nushell (a'ka, it opens new tab in the current dir). Can someone tell me how Nushell wants to be informed about the dir in which to open?

I looked into this a bit and it doesn't appear the nushell looks for or knows about an environment variable called PWD on startup. Although, I did notice that when set_path is called it sets the PWD env var. I'm guessing that somewhere in nu-cli/src/cli.rs, perhaps in the fn cli() one would need to check the PWD env var and use it if found, for this functionality to work like you want it to.