When deleting a theme, are the theme customizer settings also deleted from the database?

Short answer: No, your settings will not be deleted. They will be available next time you install the theme.

Long answer: There are 2 ways a theme can store its settings in the database: options and theme_mods. If they use options, then inside the wp_option table in the database there will probably be an option called {$theme-name} or {$theme-name}_options etc. It’s up to the theme author what option name they choose.
If they use theme_mods, inside the wp_options table in your database there will be a theme_mods_{$theme-name} entry containing all the options.

When a theme gets deactivated these options are not deleted by default, and WordPress keeps them there for future use.

There is a way for themes to delete their options on deactivation (see the switch_theme action) but it’s rarely used and there’s no reason any theme author would use it to delete the theme settings on deactivation – unless it’s a custom use-case.

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