First question is why do you want a forge ? Knowing the feature you need out of it is what should drive your decision.
Personally I would question the benefit of allocating ~5% of your work time to anything that isn’t core building your product but that’s up to you.
Yup, for a solo project that you don’t want to share I would even argue that a forge is close to pointless.
Any ssh remote will work as a backup, you can run the ci/cd task on your own computer just fine (very likely faster even), you obviously don’t need to send PR and request code review to yourself and if a TODO.md isn’t enough to keep track of tasks there’s a billions lightweight task/note tracker.
I use github because I’m a lazy and it works fine as a backup but I don’t need 99% of the features for my pet projects.