Is there a way to link my google account to my Demiplane one, so it just automatically signs me in when I go to the webpage?
Lots of other apps do this, have Single sign-in with Google. Just gets annoying to have to keep constantly typing in my login information when I use Nexus
Yes, there is! When you go to the sign-in/sign-up page, you should see an option to use either your Google, Facebook, or Twitch account. If you already have an account associated with your gmail for that Google account, you should be prompted to merge the two when you log in with Google for the first time, which lets you use either your username/password or Google authentication. 
What if my existing account is not asssociated with that gmail? Will I still be able to merge them together?
I don’t want to get stuck with two different accounts and no way to merge them, especially because my non-google Demiplane account that I currently have is the one synced to my Paizo account
I just tried and instead of letting me merge them when I try to sign in with Google, it says “That username is already in use” when I try to enter my existing account information.
When I originally signed up, I used a different email provider than google when I created my Demiplane account
I don’t see a way to change the associated email my account has, either.
Ah yes, we can help you switch over your email address for your account. Send us a support ticket with your current account information and your gmail address and we’ll switch that over for you: https://demiplane.zendesk.com/hc/en-us/requests/new