From Turbo Tax:

Found property and money is considered taxable income and needs to be reported on tax returns. Both cash and tangible property are taxable, and the fair market value of the property should be reported. It’s important to document the discovery of found property and keep detailed records of any subsequent sale or transfer of ownership for tax purposes. Donating found property to a qualified charity can be a way to lower the tax burden.

So yes, you claim found money on your taxes. As for the legality of keeping that money, that would never be a blanket correct answer, it would always depend on the particular conditions in each instance.

https://turbotax.intuit.com/tax-tips/general/what-to-know-about-taxes-on-found-property/L9BfdKz7N