123V is not going to hurt anything that was meant to run at line voltage. If that UPS is glitching and cutting out a few percent over voltage, you’re better off without it. How often does your power cut out comparred to how often this glitch happens.
It’s my understanding that uniteruptable power supplies are supposed to protect you from spikes, voltage drops, and power loss. Yours should not be acting this way.

Make sure you get a good one that will protect from surges and spikes, and keep power pretty even.
You need a Surge Protector................
Which model did you have? I had a CyberPower and it should act as a junior voltage filter itself. 124V should NOT trip it up.
That said, the front panel got wonky after a short while, and while it did fine on power interruptions, the battery wore out quickly. I went with an APC this time.
Your UPS Battery may be getting to the end of its life and needs replacing...........
Not sure what the specs on your UPS are but some sort of line voltage conditioner before that unit would help.
125v in is ok.
If the batteries in the ups are old or weak it may be time for replacement. Weak batteries are usually the problem in a ups.
Sounds like a faulty UPS or one that has outlived it usefulness. Before I retired some years ago in IT, replacing backup batteries every three years or so was the norm...
My guess is the UPS is just bad and replace it with a new one with a good +10%, -15% input voltage range.
I do not agree that you are experiencing an over voltage issue.
You can set Cyberpower and APC UPS’ to different levels of sensitivity to incoming power. You might see where it is set, and try a lower or higher setting.
Cheap power strip will not help. You would need a regulator. Mine cost $700.
My suggestion. Get rid of your power conditioner. Something is wrong with it.
You are describing a situation where a separate power conditioner is required before the UPS.
Very common to see 128 volts as close as we lived to it. No issues, except that overvoltage situations will slowly ruin electronics. Back then I built all of my own surge protectors.
IMO, time for a new UPS. I now live with Minuteman, and they are based in Carrollton. Take a look at their training, and it will shed light on their products.
By definition a UPS should not glitch.
Are you having other problems with your electronics?
I was having appliances die and blamed it on just manufactured junk. I happened to be looking at the UPS voltage meter when I saw it jump.
I contacted the power company And the guy came right out. He took one look at the power pole and said the ground wire was failing. Fixed it right then & there and rewired the entrance connections while he was at it. No more problems.
We have a great power company. As a side note, our local postal service is pretty good too.
A proper system will ride through a voltage spike or even sustained over-voltage.
A power strip in front of the UPS will not help you.
Check the power requirements for your connected equipment. You may be exceeding the capability of the UPS. If the demand wattage is even near 80% of capability, there will be trouble as the UPS ages.
I have had tolerably good performance from Tripp-Lite and APC brand systems. All brands have large numbers of detractor reports; it just seems to be a roll of the dice as to which units will work out.
I have discarded more than one UPS.
I’d bet your batteries are weak or you have overloaded the UPS. In either case, when the unit tries to go to battery backup mode due to high line voltage, it will just turnoff.