I think it's a bit of a stretch to lump "failure to budget properly" under "mental illnes".
If you're just blowing through money too quickly, then that's not really a crisis that needs intervention from the state, imo. You'll either learn to spend your money better or learn to like ramen.
I'd say if you blow through your money consistently to the point of having to eat ramen all the time, that is a problem. And it's caused by bad decisions your mind makes. So while it might seem like a bit of a stretch, it could be considered a mental illness.
A bit, perhaps. But it's not unreasonable to me. How would you define mental illness? Where do you draw the line?
At that point we would need to investigate to see if this failure is being caused by mental illness. Treatment would be much easier if our current homeless shelters could use their infrastructure to help people like this. They take your UBI check and give you a place to stay, treat you for drug addictions, etc etc.
Either that or you end up in jail, because making homelessness illegal would not be so immoral under a UBI system.