You have written some application code de novo. This code is linked to the Microsoft .net runtime libraries, which are themselves under an MIT licence (as you, and others, note above). You intend to distribute this as part of a commercially-available appliance, running on a Raspberry Pi which will itself be running Raspbian (now known as Raspberry Pi OS). You want to know what your licensing obligations are, and particularly whether you have any obligation to distribute your code under a free licence. You also want to know whether you have any obligation to pay the upstream providers (of, eg, Raspbian).
Looking first at your executable, the MIT licence on the .net core libraries does not oblige you to open up the source of your application. The mere fact of your application being distributed alongside GPL code (including, but not limited to, the Linux kernel) doesn't extend GPL obligations to your code, which is either merely aggregated with it for the purposes of distribution, or falls under exceptions such as the kernel's syscall exception.
However, you are still distributing a whole selection of free software, some GPL, some under more permissive licences, when you distribute your appliance. This will impose certain obligations on you with respect to provision of source for that free software, labelling, preservation of notices, and the like. We cannot possibly list all those obligations here; it's your responsibility to know and comply with them.
You are not obliged to buy any sort of commercial licence to use Raspbian or Chromium in this way.
And finally, of course, IANAL/IANYL; if you're going to bet a business on this strategy, you should consult a lawyer professionally.