Despite what electrical engineers would claim, I think it's very under-studied under a modern lens. When people ask for good places to get started I usually tell them to just look at what game developers are doing for pathfinding. Autorouting sort of a form of multi-agent pathfinding, so there are a lot of relevant concepts from that area.

The tension in autorouting IMO is people generally want something ideal that passes all design rule checks. My thinking (and IMO the more modern way of thinking) is that fast algorithms, fast feedback loops and AI participation are more important.

There are also a lot of relevant algorithms in VLSI/chip design, the folks at OpenROAD seem to have good stuff although I'm not intimately familiar.