Perhaps not. Capitalization is essentially the practice of reporting a large expense on the company's balance sheet rather than on the company's income statement. This is possible because most large purchases -- such as cars or machinery -- remain assets owned by the company that could be sold for cash at some later date.
Not all expenses can be capitalized. Generally, an expense should only be capitalized if its value is retained in the form of an asset. As you indicated in your question, you sold the home in 2022. Perhaps the better option is to add the expenses of the rehab to your cost basis when determining your gain or loss from the sale of the home. In such circumstances, because the home was sold in 2022, there would be nothing to report on your 2021 return.
Moreover, the above comments are based on the assumption that you are in the business of buying, repairing/remodeling, and selling homes. If the sale of the home was not connected to any business that you own, then the analysis may be different.
@jojobob
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