Is there a way to set either claude.ai or copilot.microsoft.com as a search engine in your browser? I.e., I can write a prompt in the address bar and it opens a new chat and answers that in a new page? I can do it with lots of search engines and websites (amazon, wikipedia, etc), but it seems that claude and copilot do not have a GET endpoint that let's you do it. Is there a way to do it, even through a middle page (say using javascript redirect)?
For Microsoft Copilot, simply visit https://www.bing.com/chat?q=please+introduce+python+to+me+briefly&sendquery=1, where the parameter q is your prompt. (Although it doesn't seem to "start a new chat" as you've requested)
Since I personally do not use Claude, I'm unaware of its shortcuts. However, you can always write a UserScript that checks for your prompt in the url and inserts it into corresponding chat platform.