If you are talking about the stock radio, the radio has to be "told" the VIN of the car. LEXIA and some other scan tools can do that. If it's an after market radio...sorry, good luck. Things that make you go "Hmmmm". If it's the original stock radio...why does it need to be coded back in? Or is it working fine and you just wanted to know what the "code" is? Hope that cleared thing up for you.
There are 3 parts to the key. The blade, the transponder and the remote transmitter. The blade...well that's easy. The transponder is used to start the engine. The remote, locks and unlocks the doors...remotely.
That blurb on "How to program...remotes" is only to re-synchronize remotes that the BSI already "knows". And it is only used for the remote central locking, not the engine. If a (second) key is not used for a while it will get out of synchronization with the "rolling code" used by the BSI and will need to be re-synchronized. That process does not work on transmitters that are not already known to the BSI.
Creating a key to start the engine requires the 4 character engine ECU PIN code. On early models, that was provided on a credit card sized...card...found in the owners' wallet along with the owners' manual. But they no longer do that.
Apparently there was a law passed that required previous owners of PSA cars to throw away the spare key and the PIN card! That's a joke, but explain to me why second hand cars only come with one key! Particularly seeing as the keys are @#$%ing expensive to replace.
You have a couple of options:
Ask Peugeot for the PIN, however they are not obliged to provide it. Brisbane Citroen REFUSED out right to provide the PIN but would code in keys etc. I believe that this is a franchisees prerogative but I'm not sure. Your local may provide it.
There are scan tools that can get the PIN from the BSI (LEXIA can't do that).
Hack into the EEPROM of the BSI. There are companies that can do this. However it would probably cost about the same as Peugeot providing a new key (not exactly sure on that).
The keys use an ID46 transponder (as you said). Again, these chips are used to start the engine. I have found those transponder chips in the Chinese knock off keys to be hit-and-miss. The stand alone ID46 chips seem to work fine.
The central locking transmitter. Oh boy! If the transmitter uses the 73373067B/C PCB...forget it. Buy a new key from PSA. Having said that I am not sure that they are still available!! Those Chinese knock offs DO NOT WORK on the CAN-VAN systems. Apparently they Do work on the "all CAN" systems.
Locksmiths. It's been my finding that most locksmiths do not handle this kind of stuff. I could not even find a locksmith that carried VA2 key blades! However, I got VA2 blades from Aliexpress and had them cut by Mr Minute without any problems. Now I'm talking proper automotive locksmiths. Some can code a transponder with their scan tool if you provide the PIN. An even smaller number have a scan tool to find the PIN, BUT they are very few! Maybe in Sydney and Melbourne, but not here in Brisbane. Well none that I could find. The other thing is that these locksmiths ask a premium for their service, making a genuine key look more attractive. Remember, locksmiths could possibly create a key to start your engine but they CANNOT create a key that REMOTELY opens the doors. Again, making a genuine key look more attractive.
Are there people who can do this stuff? Well there is Peugeot/Citroen. There are also a VERY small number of people who do this stuff BUT they are VERY hard to find. They do not advertise and typically do subcontract work for mechanics. I had reason to get similar work done on a Holden Rodeo. It took months to find this guy and when I did, he could not do the work for another 2 weeks as he was too busy. I wonder why?
By the way, these guys are NOT "chip tuners". People who do "chip tuning" are a dime-a-dozen! This is a completely different thing!
Sorry for the length, but as you may have guessed I have invested a lot of time and effort on this subject.