Basically as the title says. We have semi frequent power outages where I live. The noise machine in my daughter’s room goes out and wakes her up. If I were to buy a USB powered one, plug it into a power bank like one of those 10000ma ones you get for charging cell phones, would it have continuous power. Basically like a cheap UPS
Most power banks can either provide power, or be charged, not both.
They actually make what you want however, you can get usb UPS modules. They are intended for raspberry pi power, but just present a usb socket. They hot switch between external usb and internal batteries, as required.
That’s old power banks from decade ago. Majority if not all reputable powerbank brands now have charge passthrough.
Some will charge your device to full first, then disconnect the device and charge itself second.
Some will slowly charge both the device and the powerbank itself (I emphasize the Slowly part, probably at 5V 0.5A).
For OP, look for something on the packaging that indicates it have the mentioned above function.
HOWEVER! No good powerbanks will work as a UPS. Because they have built-in protection that will disconnect the power when fully charged or turn itself off when the plugged in devices is full.
I said “good powerbanks” because cheap, no-name one doesn’t have those protections and will keep on trickle charging both itself and the devices, which is really bad.
Also, as a rule of thumb, you DO NOT want to plugged in your lithium battery at all times and keep it at 100%. That’s the recipe for disaster waiting to happen.
A cheap or 2nd-hand acid-battery UPS can be bought for as little as $30-$50 on Ebay, even the smallest one will be capable of powering the noise machine for days.
That is definitely still a premium power bank feature. I’ve got a few newer ones that have full pd capability etc and they still don’t do both.
Lithium ion are fine in a UPS capability, they just need to be treated right. What most do is pass through to a boost buck converter. The external power passes through via a diode. When the external drops, the battery takes over instantly. Critically, when powered, the li ion is effectively disconnected.
Raspberry Pis often require this capability, so most usb UPS units mention raspberry pi, making it a useful search finder.