Is it correct that a Solo 401k only allows me to contribute based on my self-employment income?

Yes, that’s absolutely true.

You cannot contribute any additional funds from full-time employment elsewhere or any other funds not related to self-employment. Your Solo 401k’s biggest benefit is that you are able to roll over existing funds. If you have a lot of self-employment income, you get an additional benefit of being able to reduce your taxable income by making big contributions.