Or they could go hypermonarchist and have the child be genetically engineered from both parents.

That would have made the Middle Ages really weird.

This is the Habsburgs, they can afford a surrogate

I see someone hasnt watched Young Royals

The Romans made it work, though. From ChatGPT:

The Roman Empire is the clearest example of adoption used deliberately to choose capable successors:

Nerva → Trajan
Nerva adopted Trajan, a respected general, who became emperor in 98 CE.
Trajan → Hadrian
Hadrian was adopted (likely on Trajan’s deathbed) and succeeded him.
Hadrian → Antoninus Pius → Marcus Aurelius
A chain of adoptions: Hadrian adopted Antoninus, who in turn adopted Marcus Aurelius.

👉 This era is often called the “Five Good Emperors,” largely because merit-based adoption worked better than hereditary succession.