Sadly, based on the list of requirements, there are zero radios made today that will meet all of them.
What brand receivers do you currently own?
There are NO radios made today that have two throttle sticks.
The only brand of radio i am aware of that will provide 16 channels, do not use OpenTX/EdgeTX, and are priced less than 250 gbp are a couple models made by FrSky, and use their own firmware called "Ethos". They all support multi-protocol modules.
Frsky Twin x14
FrSky Twin X lite
FrSky Horus X10 express
Frsky Tandem X18
There may be others, but those are all i can think of right now that have Ethos firmware installed, and are below the 250 limit. There is an "Ethos Suite" software package that only runs on windows, and it allows you to backup radio models, and update firmware for the radio. it does not "simulate" the radio. All ethos radios support 24 channels on 2.4ghz frsky receivers, and up to 16 channels on other receivers, depending on receiver, using the multi-protocol module. FrSky does make less expensive radios, but they all run OpenTX.
In the "under 250" group, there is also the FlySky Paladin, i believe it supports 18 channels, but it does not support anything but their own flysky receivers, and it offers no companion like software.
There are multiple different transmitters well below your 250 limit, but they are missing lots of items from your list, ie, less than 16 channels, no pc software, only proprietary receivers, store 10 models, etc.
Other brands that support up to 24 channels include Futaba, Spektrum, Jeti, Graupner and a few others, but they are all much more than 250 gbp, and only Jeti has anything remotely like a companion, but it also does not support simulation, only backup of models, and updates of firmware for the radio. All of these manufacturers also delineate their models by price AND functionality, so their lower cost models may not support 16 channels, but even then, we are talking models that cost 400 to 800 gbp