My environment is Ubuntu 24.04.1 LTS with GNOME version 46 on an Acer Aspire A515-46 laptop.
I had been using PyCharm 2022.3.2 (Community Edition), which I had pinned as a favorite to GNOME's dock. The other day I updated to PyCharm 2024.2.3 (Community Edition) and presumed that the pinned favorite would automagically be updated along with it. It turned out that it wasn't. And I cannot for the life of me figure out how to get it to point to the new version.
To begin, I unpinned the favorite, ran the new version of PyCharm from the command line, and then pinned its (running) icon to the dock. But when I quit and tried to use the new favorite, it fired up the old version (viz. 2022.3.2). Likewise, if I'm running the new version (which I must start from the command line) and right click on its icon in the dock---whether it was a pinned favorite or merely a running app---and select "New Window," that new window comes up running the old version.
I have installed dconf Editor in the hopes that it would provide a means of editing whatever link is making the dock's PyCharm icon point at the old executable, but I have found no such feature. Indeed, it's disappointing how little Google finds when I ask it to search for things like "configure GNOME dock favorites."
So, where are the GNOME dock's current favorites stored so I can edit them (more than simply creating and deleting them). Or else, by what magic twiddling of the GUI can I rid GNOME of the misconception that when I ask it to fire up PyCharm, I still want to use the old version? I hesitate to uninstall 2022.3.2 for fear of what might break.
[Having now found my own answer (provided below), I have added the tag .desktop, since--although I didn't know it when I posted the question--that was the key to its answer.]