I use self-hosted Jitsi for screen share, although this is just video conference software without the IM aspect of Discord. (Jitsi does have IM to be clear, but it’s a chat tied to a particular meeting, not like a persistent groupchat.) You could just use Signal chats as you have already been doing and send Jitsi links when you want to call. Jitsi has E2EE although I’m not up to date on the details of how it works.