Is STD pay included in my w2 from my employer if it was paid through regular payroll? On my check it was listed as std earn-txbl under my regular earnings?

Short-term disability benefits are taxable when the premiums are paid by your employer. If you receive these benefits through payroll with your pay checks, they are already included in your form W-2. Just enter your form W-2 in TurboTax. You do not need to report these benefits separately.