If Radzig goes thru with the “paperwork” of accepting Henry as his bastard son then he will be ennobled. It is just a formality now as the fact is now widely known.
I would hafta research it but there were some “bastard” children of nobles that rose to power. over the centuries.
Yep, plenty of bastards ended up inheriting through history. Most famous, of course, was William the Conqueror - otherwise known as “The Bastard”. But, you’re right. Laws varied from realm to realm and either the crown laws or Papal edicts could deny such inheritance in specific regions. Within the Holy Roman Empire it was generally possible, but as each realm within the HRE had their own laws, it’s hard to say. Wenceslaus comes from a line sired at one point by a bastard, for what it’s worth.
That said, the game may have thrown the term “squire” around too loosely via a poor translation or something. Later on Hanush says Henry is Capon’s Page, which is a step down from Squire. Henry also claims that Radzig is giving him a steady wage, when I personally haven’t seen anything of the kind. The entire thing is pretty muddled.
Many bastard born children to nobles even came to start their own cadet-branch of their noble parents house. So Henry becoming a noble is as you have said not difficult to believe and should be a choice in this games DLCs or future games from WH. Without spoiling for anyone, Henry would probably have been named a knight in this game because of his actions and how important he is to solve many of the other nobles issues.