Can I claim as a dependent my 24 year old grad student daughter if we pay $1500/mo for student housing, even if she earned $8k in 2024 and had to file a tax return?

Sorry--no.   She is too old to be a qualifying child and earned too much to be a qualifying relative.  She cannot be claimed as anyone else's dependent.

WHO CAN I CLAIM AS A DEPENDENT?

You can claim a child, relative, friend, or fiancé (etc.) as a dependent on your 2024 taxes as long as they meet the following requirements:

Qualifying child

• They're related to you.
• They aren't claimed as a dependent by someone else.
• They're a U.S. citizen, resident alien, national, or a Canadian or Mexican resident.
• They aren’t filing a joint return with their spouse.
• They're under the age of 19 (or 24 for full-time students).
• No age limit for permanently and totally disabled children.
• They lived with you for more than half the year (exceptions apply).
• They didn't provide more than half of their own support for the year.

Qualifying relative

• They don't have to be related to you (despite the name).
• They aren't claimed as a dependent by someone else.
• They're a U.S. citizen, resident alien, national, or a Canadian or Mexican resident.
• They aren’t filing a joint return with their spouse.
• They lived with you the entire year (exceptions apply).
• They made less than $5050 in 2024 (not counting Social Security)
• You provided more than half of their financial support

@xmasbaby0 is correct.

The IRS defines a dependent as a qualifying child (under age 19 or under 24 if a full-time student, or any age if permanently and totally disabled) or a qualifying relative.

Your child is permanently and totally disabled if both of the following apply:

• Your child can't engage in any substantial gainful activity because of a physical or mental condition.
• A doctor determines the condition has lasted or can be expected to last continuously for at least a year or can lead to death.

Once your child is 24 years of age or older, and not disabled, they no longer qualify as a dependent unless they meet the gross income test, just as any other adult relative whom you support. See IRS Publication 501 for more information. Gross income is the total of a taxpayer's unearned and earned income. 

If their gross income was $5,050 or more for 2024, you can't claim them as a dependent unless they are disabled. Adult children 24 or older can be claimed as Other Dependents but will have to meet the gross income test. 

@scottlenal