Managed to sort it out, so in case anyone else reads this and needs a few tips this is what happened. I did use the Apple migration tool and just about everything moved to the new computer, but not the Silicon Labs driver.
Initially every time I tried to download the latest driver I just downloaded a text file - eventually I read something that said right click on the S Labs link, and that downloaded a driver zip file.
At this point, make sure the data logger is not connected to the computer - that stopped the installation in my case.
After opening the zip file and moving the dmg file to the desktop I could click on the dmg file and installation started.
Then Sonoma paused the installation and would not allow an extension to be loaded. There was a prompt telling me this and linking to the Privacy area in settings - unfortunately it didn't take me to just the right spot but after a bit of experimenting I found - in the extensions menu - a line that said the Silabs extension had been blocked and an "allow" button - after clicking that it all went smoothly and everything works properly. The previous Weathercat data had migrated to the new computer, the data logger updated Weathercat with the last few days so nothing lost.
Hope it helps somebody.