Existence doesn't store a separate password — you sign in using your existing Google or Apple account. That means your Existence login password is managed entirely by whichever service you used to sign up.
To update it, head to the account settings for the provider you created your Existence's account with:
Signed in with Google — Update your password at myaccount.google.com/security
Signed in with Apple — Update your Apple ID password at appleid.apple.com/account/manage
Once you've updated your password with Google or Apple, that change takes effect the next time you sign in to Existence — no action needed on your end inside the app.