Call attachBehaviors or similar so third-party Javascript runs on each page

The Svelte app is, by design, not extensible or overridable, and the pagination (I assume that's what you're referring to?) is internal to the Svelte app. So although I'm not an official maintainer of this module, I'm guessing this is most likely a won't-fix.

Tentatively closing this under that conclusion, but feel free to reopen if there's more to be said here.

To be clear, my module adds a Javascript file to the PB page. That JS file adds download buttons to eligible modules. That works on the first page, but if I click the pager to go to Page 2, Page 3, etc my Javascript isn't run: the attach method isn't called.

It seems bad design to have something in Drupal that isn't extensible: everything else is. If you add JS to a Views page, the JS's attach method will be called when you go to Page 2 etc.

My workaround is to poll every two seconds and add my buttons if they haven't already been added. That's suboptimal but I can deal with it if necessary.

Like I said, I'm not familiar with Svelte, but is adding in a hook or calling Drupal.attachBehaviors out of the question? Feel free to close again if that isn't going to happen.

I very much doubt it's going to happen.

Not everything in Drupal can, or should, be extensible. Extension points should be well thought-out and have well-defined boundaries and fences around them, to prevent messes and ensure backwards compatibility.

That said, Project Browser is an opinionated UI and all of its extension points are all on the backend side of things.

If you really want to override the way installation works, I'd suggest hacking it on the backend by taking over some of the routes defined by the ProjectBrowserRoutes class (specifically the "begin", "require", and "apply" routes).

These are not true extension points, so you're pretty much on your own and Project Browser cannot guarantee that it won't inadvertently break your overrides later, but if you insist on doing it, that's what I'd do. Trying to modify with the UI side of it is just going to lead to frustration.