Why the bypass transformer input is fed from Normal LV Switchboard and the rectifier transformer is fed from Emergency LV Switchboard? If so, how the outputs are synchronised?
Not sure I've pictured your setup correctly, but often the bypass is there for maintenance purposes - i.e. to keep the loads supplies when something (anything) in the normal chain of supply is down for any reason - including times when the downtime exceeds the duration the UPS can supply for - so it's quite usual to have the maintenance bypass sourced from a supply that's as separate as possible from the "normal" supply.
SMALL UPS units simply require plugging like any other appliance.
Larger installations are more complex and require careful design, preferably by a UPS specialist. Use of two different mains supplies for the "normal" and the "bypass" inputs is common practice to facilitate maintenance of the switchgear.
These two supplies MIGHT not need to be in phase, but this depends on the internal design of the UPS.
It is most unlikely that a standby generator will run in phase with the public supply.
Do you have a diagram for the kind of thing you have in mind - I am not sure if the below answers the question you mean to ask?
Clear'y anything that is going to be rectified (converted to DC) dopes not need to be synchonous. The UPS output is an AC created by chopping the DC, be that from batteries of from the rectifier, To make those switches synchronous to the incoming bypass AC prior to switching over is relatively easy.
And then transformer isolated, so there is no shared neutral issue, and then rectified, so any phase error is also lost, so there is nothing that needs to be synchronised, and the emergancy supply can be anything from a DNO main to a local genset.
