I think you have two questions there.
Q1. Does he really get the recovery rebate?
A.1. Yes, if he does not qualify as you dependent for 2020?
Q2. Does he still qualify as your dependent, the year he graduates?
A2. Maybe. As your surmised, yes, he must have provided more than 1/2 his own support, to not be a dependent.
Graduation year
If he/she was a student (under 24) for parts of at least 5 months and lived with you for more than half the year, and did not provide more than 1/2 his own support for the whole year, you can still claim him.
The real question is who should be claiming him in this "transition" year to adulthood. You two have to agree on who is going to claim his exemption. Each should do their taxes both ways and see which way the family comes out best. Even then, you have to meet the rules. The rule is that a child of a taxpayer can still be a “Qualifying Child” dependent, regardless of his income, if:
- he is a full time student under 24 for at least 5 calendar months of the year (graduating in May usually means you meet the 5 month rule)
- he did not provide more than 1/2 his own support (scholarships are ignored in the support calculation)
- lived with the parent (including time away at school) for more than half the year
So, it usually hinges on "Did he provide more than 1/2 his own support in 2020.
The support value of the home you provided is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants. IRS Publication 501 on page 20 has a worksheet that can be used to help with the support calculation. See: http://www.irs.gov/pub/irs-pdf/p501.pdf
