If you are positive that you have IE set as your default app for web browsing then the only thing I can suggest is setting something else (other than Edge) temporarily to see if that forces things to open in the chosen browser, then switch it back to IE.
There is no reason for anything other than Cortana initiated web searches to open in Edge if you have reassigned your default browser to something else. It sounds like although it's showing IE as your default that something under the hood didn't actually "take." If switching it to something else doesn't make the behavior change then I'd suggest running SFC and DISM (more details later, if needed) to see if you have some sort of system file damage/corruption that can be repaired. -- Brian
Here is a test to find out whether your mission in life is complete. If you’re alive, it isn’t.
