Interesting question! The equilibrium constant for this reaction is around 2 at 20°C:
Dul’neva, L. & Moskvin, A.. (2005). Kinetics of Formation of Peroxyacetic Acid. Russian Journal of General Chemistry. 75. 1125-1130. 10.1007/s11176-005-0378-8.
If [H2O2] = 0.44 M and [acetic acid] = 0.42 M and [H2O] = 55 M, then [peracetic acid] = 0.0065 M at equilibrium
which is just enough peracetic acid to provide some extra antiseptic activity. It’s also enough to be irritating but I doubt it’s a serious hazard. Perhaps others are more familiar with this hazard?
These authors also report the enthalpy of reaction as -14 kJ/mol, which allows one to calculate the enthalpy of formation of peracetic acid as -400 kJ/mol.
That is a common mixture for intentional biocidal cleaning. At those already diluted concentrations, there should be no particular harmful effect. BUT, just as with the vinegar and peroxide (in particular) you should always take care to avoid prolonged exposure. But as a cleaning mixture, it will remain as stable as the peroxide itself and poses no danger of explosion or corrosive action in the container. A site with some good usage cautions - again, mostly for concentrated solutions. Peracetic Acid Uses and Hazards
P.S. I also made my own formulation of 3% hydrogen peroxide and 70%propyl alcohol (50/50) as a great deodorizing cleaning spray for dogs urinating were you don't want them, and particularly for cleaning rugs and fabrics.