Hello guys, just stumbled across this thread.
The only launcher that works correctly on 10.9 without any real issues is the legacy .jar launcher paired with Java 8, which you may be familiar with if you've played Minecraft before ~2016. However, the first roadblock that you'll come across is the lack of MSA authentication. Fortunately, someone has created scripts to add Microsoft Authentication to the legacy launcher:
https://github.com/NepNep21/MSA4Legacy
I've also attached the patched launcher as a file, but feel free to run the scripts manually from GitHub.
Once logged in through MSA Authentication, you can run any version of Minecraft up to and including 1.16.5. 1.17+ won't run as Mojang bumped up the required Java version to 17, which I haven't been able to get running, even with wowfunhappy's excellent dylib stubbing guide.
I've done some brief testing with the MSA Authentication patches, and everything seems to be working correctly. I've even been able to play on some major servers such as Hypixel.
Enjoy!
Edit: hrrmm, took a closer look at this thread and looks like OP already got the modern launcher working. Oh well, I'll leave this here if anyone wants to take a look at the legacy launcher