Generally the best approach is to avoid situations like this through normalization. However, when that is not possible, you can write a script to do the search for you (though it can take a long time to run against a large table.)
I once ran into a similar issue with a denormalized table and wrote a script to handle the search for me, and then wrote it up for SQLServerCentral at https://www.sqlservercentral.com/articles/finding-values-with-numerous-columns
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