Turn out, all I needed was to remove "launchAutoHide": false option from my capacitor.config.json. In my case, it was already set to false, though. From the capacitor documentation:

Hiding the Splash Screen

By default, the Splash Screen is set to automatically hide after 500 ms.

If you want to be sure the splash screen never disappears before your app is ready, set launchAutoHide to false; the splash screen will then stay visible until manually hidden. For the best user experience, your app should call hide() as soon as possible.

If, instead, you want to show the splash screen for a fixed amount of time, set launchShowDuration in your Capacitor configuration file.