I refinanced my original mortgage and HELOC this year into one new mortgage. Do I count the new mortgage as a "Cash out refinance" since I consolidated both old loans?

No,  When Tax Cuts and Jobs Act was signed into law in 2018, one of the deduction that was suspended was HELOC (Home Equity Line of Credit)  mortgage interest made after December 31, 2017, and that made it fully non-deductible.  The original loan used to buy/build a home up to $750,000 for married filing joint ($375,000 for married filing separate) was still fully deductible. The new mortgage needs to be prorated.  For example:

• Original loan                            $ 600,000
• HELOC                                       100,000
• Total                                             700,000
• Percentage                                      83%
• Mortgage interest/new loan         $20,000
• Deductible mortgage interest      $20,000 x 83%   = $16,600