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All you can really do is try the launcher again every time it gets updated, which is about every 8 weeks or so.
Do you know for sure that the current launcher version 2022.14 still doesn't work on macOS versions before 12? @BraydenKL's launcher-dowser.log shows that dowser is installing the launcher version 2022.12 which is shipped with eu4. Trying the installation again won't help even if there is a fixed launcher unless eu4 also gets updated to use the new launcher. In the past you provided download links for launcher installers. If version 2022.14 or a future version fixes the problem,such a download link would enable users to update the launcher even before their game is updated.

@BraydenKL in the meantime, there is an untested workaround which will probably work:
  1. delete ~/Library/Application Support/Paradox Interactive/
  2. downgrade eu4 to a version which contains a launcher which still works on your macOS version. I think 1.32.2 is a good bet
  3. start eu4 from steam to install the launcher
  4. confirm that the launcher works and then immediately close it so it can't update itself to a broken version
  5. now you have to avoid the auto-update in some way. One of the following will probably work:
    • block the paradox update website in a firewall(but this could also block the paradox login)
    • let the upgrade happen, but delete the installation folder of the new launcher version each time before you start eu4. I don't know the exact folder, but it should be somewhere in ~/Library/Application Support/Paradox Interactive/
    • prevent the launcher from installing the update by creating the folder which it wants to use and then making it read-only. Making the parent folder read-only might also wrok
  6. confirm that the launcher still works
  7. switch back to the current eu4 version
Another option is to start eu4 without the launcher. You could use an alternative launcher like Irony Mod Manager or you can start eu4 directly from its installation folder or you can modify the a launch options in steam to bypass the launcher. The first two options might require that you create a steam_appid.txt in the eu4 installation folder which just contains "236850" (without quotes). Otherwise eu4 might not be able to verify your DLCs with steam.
 
Do you know for sure that the current launcher version 2022.14 still doesn't work on macOS versions before 12?
Yes, I get cases like that almost every day. They are still looking into it, as they can't reproduce the problem.
 
Yes, I get cases like that almost every day.
But do you get cases with the current launcher version? People who have the problem can't update their launcher and uninstalling brings them back to the version which is shipped with their game. Even the 1.1 version of victoria 3 which came out three days ago still ships launcher version 2022.12 (at least on Linux).
They are still looking into it, as they can't reproduce the problem.
Do they have a macOS 11 computer which doesn't have the javascript error with one of the affected launcher versions from one of their games(e.g. 2022.9 from eu4 or 2022.12 from ck3/vic3)? Maybe there is something installed on that computer which avoids the problem and the affected users could install that as well.
Or they just don't understand why their build system generates launcher binaries which don't work on older macOS versions? Or did they maybe not test the launcher which comes with the games and their development version works differently?

@BraydenKL I just realized that you play ck3 and not eu4, so my previous instructions might not have been so helpful. But I saw that you own cities skylines which ships with a very old launcher version from 2020. So you could delete ~/Library/Application Support/Paradox Interactive/ and then start the current cities skylines version to get an old launcher which should definitely work on an older macOS. You could also try to let that old launcher update itself and see what happens. It should go to 2022.14 with one or two intermediate steps, but it should bypass the other 2022 versions. So maybe 2022.14 works for you. Please let me know if you tried one of my suggestions and if it worked or not.
 
But do you get cases with the current launcher version?
Yes.
Do they have a macOS 11 computer which doesn't have the javascript error with one of the affected launcher versions from one of their games(e.g. 2022.9 from eu4 or 2022.12 from ck3/vic3)? Maybe there is something installed on that computer which avoids the problem and the affected users could install that as well.
Or they just don't understand why their build system generates launcher binaries which don't work on older macOS versions? Or did they maybe not test the launcher which comes with the games and their development version works differently?
I can't answer these questions; you could ping @Deuterium Oxide in a new thread in the main from here, or via PM.