I recommend including the version of Anki that you’re using. Or better the whole debug info (Anki > About Anki > Copy debug info). The crash report of macOS doesn’t include that information.
In any case, try version 25.07.3 as the crash you’re reporting was reported already a few times here and subsequently fixed.
Issues stemming from third-party packaging should probably be brought up there. However what you mentioned about installing dependencies might be due to a misunderstanding: If Homebrew doesn’t build their own Anki binaries, then they probably just install the official launcher for you.
The launcher is a small program that downloads only the dependencies that need updating. This makes it quicker to update, as big dependencies without changes (for example the Qt framework) don’t need to be downloaded again. It also allows for more flexibility in case you want to use other versions of certain dependencies. And first and foremost it solves the issue of PyOxidizer development being abandoned.
See also New online installer/launcher
Now it seems like the behavior of Homebrew that you describe boils down to, whenever there is a new Anki version, Homebrew will apparently download a new launcher for you, and then when you start it for the first time, the launcher will do the actual updating of your Anki version. Be assured that that last step is needed, as Homebrew just downloading the launcher again does not modify/update your Anki installation in any way.
However I see that it would be neater if all this could happen in one step. I see some options here:
1: Homebrew could provide an actual package of Anki instead of just helping you download the launcher. The source code is available, everybody is allowed to create and distribute binaries. This approach would forego using the launcher altogether as Homebrew would need to make sure their Anki binaries work properly on the systems that they target (mostly macOS I guess).
2: Homebrew could leave updating Anki to the launcher that it downloaded during initial install. After all, the launcher is now the official way to upgrade Anki, and auto-update functionality is included. With the launcher installed, no real reason for Homebrew to get involved anymore. (Small caveat currently being that while the launcher can update Anki, the launcher cannot update itself in case there are changes to the launcher itself.)
3: Just continue on always replacing the launcher with every new Anki version. This might be a slight inconvenience to some users, but it requires no additional effort on Homebrew’s part and also ensures the user gets the newest launcher code just in case something ever changes there.