Questions regarding setup and split tunnels?

Hi There, I have some questions regarding a setup and how Split Tunnels work.

I was playing around with Split tunnels and noticed that, with Split tunnels enabled, I would enter my local LAN subnet in there and all traffic still appeared to leave via my local gateway, also a whoismyisp showed my legitimate ISP.

However, when disabling Split Tunneling mode, I could see traffic not longer “left” my default gateway, and also a whoismyisp reported that my ISP was Cloudflare.

So my question is, if I have Split Tunneling enalbed with my local subnet added as a network, is all traffic still encrypted over the tunnel end-to-end?

Also, I would like to use WARP also as a VPN, for allowing access to remote functions however I would like to allow complete network access, including ICMP etc. Is this possible with WARP and do I need a WARP client or cloudflared running locally to achieve this?

I would like some privacy, but also be able to still access local resources on the LAN.

Whats the best mothod for this.

Thank you very much!