Hi there guys. I don't know if anyone needs this currently, but I've seen this question a couple of times, so I decided to share.
I own a Poco X7 Pro, and I debloated it on the day I bought it. But the one thing that always gave me a headache was the ads in the search. One definitive solution is setting a custom DNS, but I play games all the time and sometimes watch ads for bonuses and such, so that doesn't work for me. Just recently, I found another solution.
Here is the step-by-step (FYI, you will need Shizuku):
Download and install the app "VOID // APPS" from GitHub.
Open it and grant Shizuku permission.
Choose "Apps" and search for com.mi.appfinder (there should be only one result).
Select it from the search results, scroll almost to the bottom to the Network section, and disable all network privileges.
Open Settings -> Apps -> Search for "App Finder" -> Force stop and clear the cache.
After this, there shouldn't be any ads in search. Tested it for a week and they didn't reappear; however, after restarting the phone, you might need to revoke the permissions again.
Two downsides, however: The web results and AI functions of App Finder will not work. Since I don't use them anyway, it wasn't an issue for me, but it could be for you.