The right way to do this is to create an API or MCP or whatever catering to bots, and implement corresponding terms in your legal agreements (i.e. after approving a bot to interact with us, you're responsible for purchases it makes), along with some limits to prevent runaway shopping when Muse decides to binge.

Less friction = more shopping = more profits.

That used to be a concept companies like Amazon understood well. (As well as companies like Google in the context of web browsing and keeping it user-friendly as opposed to user-hostile).

If the bots mean customers are getting a better deal elsewhere, then you're doing something wrong elsewhere in your business model and need to go address that. Or eventually free market economics will, no matter how big an artificial moat you try to build.