A PSU hold-up time is the amount of time that a PSU can continue to output power at maximum output within standard voltage tolerances following the loss of input power. This is important for supporting UPS units because [https://www.sunpower-uk.com/glossary/what-is-transfer-time/ the transfer time] taken by a standard UPS to supply power from its battery can leave machines without power for "5-12 ms". [https://paginas.fe.up.pt/~asousa/pc-info/atxps09_atx_pc_pow_supply.pdf Intel's ATX Power Supply design guide] specifies a hold up time of 17 milliseconds at maximum continuous output. The hold-up time is a inverse function of how much power is being output by the PSU, with lower power output increasing holdup times.
Capacitor aging in PSUs will lower the hold-up time below what it was when new, which could cause reliability issues as the equipment ages. Machines using substandard PSUs with hold-up times below the specification therefore require higher end UPS units for protection to ensure that the transfer time does not exceed the hold-up time. A hold-up time below the transfer time during a transfer to battery power can cause undefined behavior should the
PER_OK signal not become deasserted to force the machine to poser off.
If in doubt, use a double conversion UPS unit. Double conversion UPS units always run off the battery, such that the transfer time is 0. This is unless they are high efficiency models that are hybrids between standard UPS units and double conversion UPS units, although these are reported to have much lower transfer times than standard PSUs. You could also contact your PSU manufacturer for the hold up time specification, but if reliability for years is a requirement, you should use a higher end UPS with a low transfer time.