If the specifications don't explicitly say whether the supply puts out a stepped square wave or a true sine wave, they still sometimes list the Total Harmonic Distortion, or THD. A pure sine wave will have 10% or less THD, while a stepped sine wave will measure roughly 35% to 50%.
Some of the first PC power supplies equipped with automatic power factor correction (APFC), probably 10-15 years ago, didn't like stepped square waves because they caused high current spikes in the APFC circuit that cause it to burn out. It wasn't just cheapo power supplies that had that problem but even Seasonic. Otherwise backup power supply compatibility depends on the total power consumption and amps (Volt-Amps) of the computer, not on the particular PC power supply.
I wouldn't trust any backup battery to last more than 3 years, and the automatic test built into most backup units will indicate that batteries are good even if they can't run a computer for 10 seconds.