Napoleon’s otl son was half German as well.
Half-Austrian. This one is half-German. It's probably more a modern thing. But also Marie Louise's parents were born (and raised) in Italy, before coming to rule in Germany. The Wittelsbachs of Auguste's branch have never really ruled
anywhere else (at least not in the last century).
I think this specifically refers to a second son. I certainly don’t consider that very exciting, but I don’t really consider dynastic politics as a whole very exciting.
What would be interesting is the political ideology and the political role such a child would play.
Well, in general the line of Wittelsbachs that ruled Bavaria up until 1777 had a love-hate relationship with the Habsburgs - they married into the imperial family several times, tried for the imperial crown once or twice (got it once, couldn't keep it though). And then comes Karl Theodor who's willing to trade Bavaria to the Habsburgs for the Austrian Netherlands, and later Maximilian I who seems to be pretty chummy with Austria in the 19th century against Prussia (where someone like Maximilian II Emanuel might've played Austria and Prussia off against each other). So, perhaps this kid would cement the Wittelsbachs into an anti-Austrian policy?
As to the political ideaology/political role - I guess it would depend. If we see an analogue of OTL events, Napoléon overreaching himself (not sure how likely that would be with a POD in 1806) and falling around the mid-1810s, Junior's gonna be a kid of at most, eight years old (in 1815). That's a little older than the king of Rome was OTL, but his mother's father is also a lot less powerful than Rome's maternal grandfather. What happens to the kid? Are Britain and her allies willing to see the kid become the new ruler of France (thanks to his grandfather's secondary power status?) or do they still pull for a Restoration of sorts? I do feel that if they punish Napoléon they'll be a lot more severe on Maximilian here (most likely he doesn't defect at the end like OTL), choosing between siding against your traditional enemy (Austria/Prussia/Britain) or your traditional ally, who also happens to be your son-in-law/grandson (France) seems like a bit of no-brainer to me. Although, admittedly, the Zweibrucken branch of Wittelsbachs seem to have been more opportunists than anything else. And the ideology or political role would depend on whether the boy is - as previously mentioned - left esconced as emperor of the French or deposed as prince of Eichstatt? If the former, he's likely to develop on very different lines to the latter.
Half-Habsburg - which prior to Napoléon and after him - ruled a good portion of Italy. Seeing little Charles (figure Nappy would name his second son after his dad) become king of Italy when he has less dynastic links to the country (I know, Napoléon didn't have links to anywhere when he became emperor, but the Italians might prefer a half-Habsburg Bonaparte king to a half-Wittelsbach king) seems a push. Hence why I suggested as a sort of German viceroy for his brother, the French emperor.
Napoléon had broken the Habsburg yoke on Italy, and while I don't see throwing Eugène under a bus, I don't see Nap giving him what is nominated as a secundogeniture for the French emperor (for all intents and purposes). So the only way Eugène would keep Italy is if his one-time-stepdad doesn't have a second son. Maybe
@Yanez de Gomera or someone else can help out here and say if Eugène might be considered as a replacement for Naples (if Joseph still gets sent to Spain) instead of Murat, while Prince Charles Bonaparte gets the Iron Crown of Lombard?
If Auguste marry Napoleon Eugene will likely marry another German princess and at least stay as Viceroy of Italy. I think who a divorce of Napoleon and Josephine at this time will very likely include in the settlement a royal or semi royal bride and his own Kingdom or Dukedom for Eugene
Suggestions? Stéphanie's doing Baden, Jérôme is securing Württemberg. Maybe Princess Auguste of Saxony? I seem to think there
was talk of her perhaps marrying a Bonaparte(-relative), but a match with Prince Joszef Poniatowski was viewed as a better option. Unfortunately it never came off. Eugène wedding Auguste and fathering the future dukes of Warsaw/kings of Poland by her could be fun. Otherwise, I wonder if Napoléon wouldn't be less interested in Eugène and thus perhaps M. de Beauharnais ends up as king of Sweden instead of Bernadotte (the original proposal, which was scuttled because someone (can't remember who) insisted that Eugène remain a Catholic rather than convert to the Church of Sweden).