Is severance pay subject to state unemployment taxes?
Depends on the state, but probably taxable. Severance pay is normal vanilla wages until/unless the government says its not. There is nothing inherent in several pay that makes it special for taxability. The one possible exception is something called Supplemental Unemployment Benefits (SUB) but that is a federal exception and requires a very formal plan like a 401(K) with a bunch of rules that must be followed.
Is severance subject to Supplemental Taxes. Can this be aggregated to their employees final pay?
If you read the IRS publications, there are several different legal Supplemental Taxation Methods. 25% Flat Tax is one, and Aggregation with the normal wages is another. Either way it is Supplemental Wages, but there are (at least) two different legal withholding methods.
Just a clarification, Under the TCJA, the optional flat rate is now 22% (down from 25%) and the mandatory flat rate is now 37% (down from 39.6%). Both tax rates are tied to the individual income tax rates in effect for the calendar year.
Severance pay is, by definition, supplemental pay. Unless the mandatory flat rate applies to a payment, the aggregate method can always be used whereas use of the optional flat rate may not be allowed under some circumstances.
Flat Tax and Aggregate are the two main Supplemental Wage Withholding methods, but there are a number of obscure methods which are rarely used and generally done incorrectly when they are used. Payroll needs a really good reason to use one of the obscure methods (IMO). I have used Annualization but it is a lot of work for no good reason (for Payroll anyhow). I have had the brass insist on it's use for them and them only, but they generally do not like results and then usually insist on using an illegal method of their choosing. Best to not even raise the possibilities. The brass wants no taxes withheld and no income reported as wages. Anything short of that leaves them unhappy. Putting in a lot of extra work that just makes the brass unhappy with results is a road best not traveled.