I'm trying to log in to Project Sigil for the first time, and when I log in with Google, it tells me I still need to create a new account with Wizards. I always sign into the website with my Google login without issue. Can't seem to get in at all and I don't want to create a new account as all of my purchases are on this one.

It does require a Wizards account (they noted on the post for it https://www.dndbeyond.com/posts/1919-what-is-sigil-d-ds-new-immersive-3d-vtt). You should just be able to create a Wizards account and link it to your existing dndbeyond account. I already had a Wizards one but I still log in with Google and that worked for Sigil as well. 

Wizards of the Coast is asking for a example@wizards.com email address...I don't have one of those, when I put my gmail address in, it says invalid. How do I check a wizards.com email address? Any suggestions? Thanks!

If I try to register for one with the email I use for my D&D Beyond account, it tells me invalid email.
If I try to register with an email that's different from my D&D Beyond account, it lets me register, but fails to link the account because it can't find my D&D Beyond account.

Also, does logging in to Sigil through Twitch prevent your licenses from synching properly?

I had to go to D&DBeyond and unlink things there before trying it again. It only likes to be attached using the WotC account. It's working now except when it flickers while I'm signing in or choosing tokens/minis. Possibly a cord issue on my end?