SRE: I think the refreshLinks.php needs to be run on the wiki because, after a manual dummy edit to one of the templates the Twinkle_Standard_Installation template is transcluded in, the lists of transcluded pages for that template immediately updated with the template I dummy-edited.
So yeah, maybe refreshLinks.php or something similar would fix it.

As a matter of fact, it looks like the remaining templates that are not appearing in the lists of transclusion for that template are not existing, whereas they are.

In T10538#212239, @BrandonWM wrote:

What are the issues in code execution? Looking at the copypaste template, I can't find anything.

I mean, I'm running an off-site script (hosted on Github Actions) checking the completeness of the templates that the Twinkle gadget will use. However, now it will return errors because of the unexpectedly corrupt template list (It was supposed to return all the results, but that was only a fraction).

By the way, is it possible for me to request a refresh for the whole site (in order to avoid other probable problems)?

I just had another problem when I was testing regular expression substitution (although it seems to have been mentioned by a previous reply), showing that the edited page doesn't exist (but they do), it looks like there's something more complicated about this? I hope that measures will be taken as soon as possible, as the magnitude of its impact exceeds my previous estimates.

Sent this reply just to confirm that this task of mine has not been forgotten...

It has not been. SRE are just busy with a lot right now, might take some time.