Your grandfather would not have paid any gift tax when he gifted half ownership of the home to you, unless the total of all gifts that he made in his lifetime was more than $11 million. Unless you think he was in a position to make such large gifts we'll assume he did not pay any gift tax.
Since you never lived in the home, you are not eligible for the Section 121 exclusion of gain. That's the $250,000 or $500,000 that SharonD007 was talking about.
I neglected to ask what state your grandparents lived in. I'll assume it is not a community property state. If it is a community property state, the discussion of your grandfather's basis below has to be modified.
Your taxable capital gain on the sale is the amount you sell the home for, minus your basis. Here's where it gets complicated. You received half of the home as a gift in 2019, and you inherited the other half in 2025. Your basis for the inherited half is relatively easy to determine. It's half of the fair market value of the home on the date that your grandfather died (not the date that he put you on the deed). If you sell it within a short time after he passed, you could probably assume that the value didn't change between his passing and the sale, so your basis for the inherited half would be half of the selling price.
It's the other half that's complicated. Since it was a gift, your basis is half of what your grandfather's basis was. But his basis has two halves. His basis for his original half of the home is what he paid for it, which would be $10,000, plus half the cost of any improvements that he and your grandmother made before she passed, and the full cost of any improvements that he made after she passed. When your grandmother passed, your grandfather got "stepped up basis" on her half the home. That means that his basis on her half was half of the fair market value on the date that your grandmother died.
Your entire capital gain will be long-term, even though you only owned your grandfather's half of the home for a few months. Capital gain from the sale of inherited property is always treated as long-term, no matter how long you actually owned it.
You might want to consult a tax professional for help figuring all of this out.
