Does anyone know if dental crowns that you pay out of pocket for count as a supplies and equipment expense?

Where?  Those are medical expenses and are deductible if you itemize on Schedule A.  

You can only deduct the amount of unreimbursed Medical Expenses you actually paid over 7.5% of your AGI.  And then all your itemized deductions have to be more than the standard deduction to get any benefit (so you would only be getting the benefit of the amount that puts you over the standard deduction).  And since the Standard Deduction is increased more people will not need to Itemize.

For 2024 the standard deduction amounts are:

Single 14,600+1,950 for 65 and over or blind

HOH 21,900 + 1,950 for 65 and over or blind

Joint 29,200 +  1,550 for each 65 and over or blind (both 32,300)

Married filing Separate 14,600 + 1,550 for 65 and over or blind

Are you talking about Medical and Dental Expenses on Schedule A? Crowns definitely belong on Schedule A.

But where does this "supplies and equipment expense" come from? Is this for Schedule C?