The proceeds from the sale of the home would have been income to your mother (likely much of it excluded as her primary residence) at the time of the sale in 2021 and won't be part of the inheritance.
From a tax standpoint, nothing has to be designated as inheritance. Nothing that is distributed under the will is income itself, and therefore it isn't mentioned on the tax return. The assets received could give rise to income later, however. For example, if you deposited your $10,000 into a mutual fund, you might owe taxes later on dividends or capital gains distributions. You will also have a capital gain (or loss) upon redemption.
Logistically, if the assets were in a trust they would need to be properly distributed from that trust by the trustee, and that will typically generate a tax document known as a "K-1".
Assets that were subject to division based on the will (or state intestacy laws) don't have a place on the tax return, but the personal representative or executor of the estate will usually need to document how they were distributed based on the requirements of the probate court supervising the administration of the estate. How that is required, and when, varies a great deal based on state law.
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