The previous developer for my org, who built 100% of all our scripts, left last summer, and it broke a bunch of things because various integrations were tied to his user auth keys. My question is, would it be sensible to create a separate super admin user for all integrations and script ownership in order to avoid that happening again, or is there a better way?

I would recommend to have a separate user/employee record for the authentication tokens only.

Always create an Integration role and an integration web services only user to create the consumer/access key tokens.

Will there by any problem if we transfer the integration role from one user to another?

You will need to create user access tokens for that user

But it wouldn't break anything as long as we redo the setup for the new user?

It will break the integration if you disable the access of the user who has left the company. When you generate new tokens, you will need to update it for all the integrations.

For next time, it might help to see all the customizations owned by inactive users which is something Flashlight by Strongpoint can show easily: https://www.strongpoint.io/flashlight-by-strongpoint