Every time I launch Caprine, it defaults to using Menubar mode (aka. shows the tray icon next to power/wifi/etc.), then I disable it, and again after a restart it is back on. Same thing happens if I refresh Caprine using cmd+R.

Update: I noticed now that if I do cmd+R the tray icon appears, but in the top menu Caprine -> Caprine Preferences -> Show Menu Bar Icon is not checked (which is correct). So the setting appears to be saved correctly but not detected by the application.

Another update: now I closed Caprine and started it again, and this same thing did not occur anymore. And not with cmd+R either.

And yet another update: rebooted the computer, and after auto starting Caprine the tray icon was there again, even though the option is not checked in Preferences. After closing and starting Caprine again manually it worked right again. Could it be that when starting macOS the tray gets initialized after Caprine, which detects that it's available and ignores the setting in that case? In this case some startup delay for Caprine would work as a dirty hack to fix this.

Version 2.44.0 (2.44.0.1789), MacOS Catalina 10.15.3, Caprine installed using Homebrew

By the way:
Auto update from 2.43 failed but didn't say anything, I noticed it by running /Applications/Caprine.app/Contents/MacOS/Caprine in terminal. Some checksum didn't match. I updated it using brew upgrade caprine.