Turbo Tax doesn't recognize "Unemplyment compensation insurance." Should I categorize it as "unemployment tax" or "other (not categorized)?"?

Your question is unclear.  If you are asking about Unemployment Comp. income, it  should go on the 1099-G screen.  If you are asking about Unemployment Comp tax (a handful of states, including NY & NJ do have employee withholdings for SUI tax), it is entered on the W-2 form.

Unemployment is put in Schedule 1 Line 7.

If you can't figure out how to do this, you need to call TT.

What form are you trying to fill out?  This should not come up when doing a 1040.

Pearl would ask a tax place.

Turbo Tax has an excellent help portal with access to ask people questions directly as well.  Asking on a bottom of the barrel site which is shutting itself down in a few days is not wise.