Played on steam to start on windows PC, Want to play on macbook through Jagex Launcher, how to find my steam login email for jagex launcher?

Hello, this might be a little confusing but definitely an issue people have run into before.

I started on steam and played a few hours, wanted to continue playing on my macbook, but instead of installing steam, I ran the game through Jagex Launcher on MacOS. The Jagex Launcher does not provide me with Steam or Apple Login (I have both connected to the first account) but the e-mail that I use for my apple login also logs into another account I made years ago with the same password and my current league character is nowhere to be found on that account.

What's the best way to get access to my account through the jagex launcher?