ZDoom

Added as a per-map feature, because making exit texts part of the cluster was a really bad idea.
There's now a complete set of properties to define intermission texts for specific transitions from any map to a specific other one.

For future searchers who happen to want to do this same specific thing, I was able to work around this by creating a custom intermission that just displays the text, the continues to the next map as intended.

[quote="Graf Zahl"]Simple solution: Use the same cluster for the secret map as for map 20.[/quote]

Ah, that only works if there's a non-secret map after 20, which there is not in this case.
To spell it out, here's what should happen when the player:
- exits map20 normally: show story text, then go to curtain call (cast)
- exits map20 through secret: go to map21
- exits map21: show story text, then go to curtain call

Simple solution: Use the same cluster for the secret map as for map 20.

[quote="Graf Zahl"]Doesn't it work if you give the secret map's cluster an enter text?[/quote]

Ah, it does, so I should've been more specific in my request: I want there to be no story text if the player secret-exits from map 20, but some story text if they normal-exit from map 20. Setting the secret level's cluster's entertext to "" doesn't work, it just shows the previous cluster's exittext.

Doesn't it work if you give the secret map's cluster an enter text?

It doesn't seem possible with the current map cluster definition system to have a different piece of text (or no text at all) if the player exits a map at the end of a cluster via a secret exit versus a normal exit. This doesn't come up with the stock Doom 1 & 2 setups because their secret levels always come in the middle of their cluster rather than on the last map, but this would be useful functionality - say, for implementing a "good" or "bad" ending in separate maps - and is not (AFAICT, looking over the [url=https://zdoom.org/wiki/MAPINFO/Cluster_definition]wiki[/url] and code) currently possible.