Is there a way to save cupcake settings the way SP settings can be saved?

The settings for all NRaas mods, or any subset you choose, can be exported (saved) and imported using Overwatch.

NRaas > Overwatch > Immediate > Export (Import) Settings

Note though that OW works with global settings (those on City Hall). If the goal is to replicate bakery rack specific settings for new bakery racks in a different world, not sure if that can be done.

If I select that I want the mod to for example only stock lemon cobbler and apple pie, will overwatch save those settings so I can import them in another town?

If you use the Random: Set Recipe Selection command on City Hall to arrange this, then yes. If you do this on an individual bakery rack basis one by one, then no.

Compare it to SP if you like. We can export/import General, Town, and Caste Options, but not Sim and Household Options (because that wouldn't make sense as they are not global).

Thank you for explaining