He would be a qualifying relative dependent (the name of the regulation, which includes non-relatives).
First, he can't be a qualifying child dependent of any other taxpayer. If he is a qualifying child of another taxpayer, that person must claim him and you can't. What that boils down to is that the boyfriend is a taxpayer, he must claim the child and you can't, because his claim has priority. Your boyfriend is a taxpayer if he has taxable income more than $12,950, or self-employment income more than $400, or files a tax return to claim any other dependent, credit or benefit. He can file a tax return and not be considered a taxpayer only if he owes no tax and is only filing to get a refund of withholding and claims no other credits or benefits.
Then, if the boyfriend is not a "taxpayer" for 2022, you can claim the son as a dependent if the son lived in your home the entire year and you provided more than half his support. You would list the child as "other" -- he is not a stepchild unless you legally married his father.
