Those are called supply chain shortages.

I'm fairly certain the actual lead times to procure semi-custom chips are indeed in the range of a few months. And a fully custom chip is a few years.

The months long lead time is not purely a scheduling/capacity issue though. Producing the masks for these modern processes is very complex and slow. Adding more fabs won't help because because its a latency issue, not a throughput issue.

The OP is talking about years-long lead times.

AFAIK (but never studied the latest processes), making a mask takes weeks. That means that the minimum lead-time on making masks is weeks long, because there is no interdependence between them. But I'm sure this is one of the steps that add up to years on practice, because of production limitations.

Actually making the chips has a higher floor, because every step is interdependent. With a hundred steps, each one taking half a day, we are talking about 2 months here. There are probably more than a hundred, and a few take more than half a day (but many take less than it), so yeah, I'd easily expect a 4 months minimum. What doesn't compare to years at all.