MacOS
Lipika IME works well on MacOS Ventura on Macbook Air M2 chip - March 2023. You will have to download the compiled LipikaIME.pkg file from it's github releases page.
Some screenshots as seen on MacOS Ventura (Mar 29, 2023).
Keyboard Ventura
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Keyboard Settings on MacOS Ventura
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Lipika settings
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Old notes:
For Mac, Let's investigate MacUIM as given by Shreevatsa. MACUIM no longer works.
Linux
Old notes: On Linux: Setting up Kannada Input on Ubuntu