You became owner of half the property on June 4th, 2022 or 2023, (you seem to say both, so maybe a typo).
Half your basis is half the value on the date you became half owner.
You inherited the other half, so the other half of your basis is half the value on her date of passing.
So if the value when you became half owner was 200,000, your half basis is 100,000.
If the house was worth 250,000 on the date of her passing, your other half basis is 125,000 so your total basis would be 225,000.
If it sold for 240,000, you would have a gain of 15,000 but then you would need to subtract selling costs. Selling costs would probably be around 15,000 depending (in part) on the commission you paid so it would be close to no gain no loss.
If you gave your brother half, (over 18,000 single or over 36,000 if joint ) you would need to file a gift tax return Form 709.
TurboTax does not support Form 709 and it is not part of your federal return.
Form 709 is reported to let the IRS know the gift was made, it usually has no tax consequences for you or the person you gifted, if your lifetime total of gift giving is less than 13.61 million single or 27.98 Joint.
Form 709 is fairly simple to fill out and can be mailed. HERE are instructions for Form 709.
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