At least in my jurisdiction (America) the only way to achieve what you are trying to achieve is by installing a dedicated subpanel fed by the UPS with appropriate breakers. I believe that such an installation would only be code compliant with a UPS that was designed for such an application (with a hard wired output connection, and appropriately designed disconnects), but a lenient inspector might let you get away with feeding a subpanel from an extension cord as long as as of the breakers and capacity factors work out correctly and the grounding meets code.
The biggest issue I see is that the system is not labeled correctly (at all?). That is a pretty serious issue because if, for example, an emergency worker were to come into the house under the expectation that the power to the house was cut (at the service disconnect) but the house would have live outlets that are otherwise unmarked. See https://www.mikeholt.com/download.php?file=PDF/11_Generators... for more information (the relevant section for your system starts at page 16)
As other commenters have pointed out, just because you can buy something that says NEC approved on the sticker does not mean that it is approved for your application. A good example mentioned elsewhere is using a 16awg SJTW extension cord to power a 15a load--all of the connectors will plug together but the combined solution is obviously not code compliant and even if it doesn't melt/catch fire it will not supply the load with clean power.
So the first question to answer is what NEC allows, but you will then need to double-check for your specific context.
Further, the power inlets are NEC approved but that in no way means that they are approved for this use. I'm far from an expert on the NEC but I can pretty confidently assert that it allows such inlets only for specific uses, and you would need to check carefully that what you propose is one of those uses. A very rough rule of thumb is that you are not normally allowed to have more than one "user-removable plug" on the path to a device. There are a number of exceptions to this, but any time you're plugging into something that plugs into something else, you need to check carefully if what you're doing is allowed.
If they sell those power inlets which are NEC approved, how can you use them without breaking code? So it MUST be code. But then you ask 10 people and get 10 answers
There are larger UPS's designed for hard-wiring, but they are almost always VERY large. I think that might be the only way to avoid an inlet cord like this