MIUI only shows ads inside apps. If your phone shows ads even when not in use, then you probably need to check what app starts in background and the permissions given when the phone boots. Different phone UI different methods.

Like MIUI : Settings - Apps - Permissions - Background auto start.

I bought my redmi note 12 Aug this year from Shopee (global rom non official store). There are ads only in xiaomi own apps like Optimize - Cleaner and Boost. Camera no ads. File explorer had small ad section. But that went away somehow.

However i did notice additional apps/ ads will come back if you install free games that are ad driven. There is something inside MIUI that auto loads similar ads that certain aps has the same sponsors to.

Its not dodgy la. Just remove all the apps you know you do not need. Some apps are baked into the UI and can;t be removed. But you can stop them from ever starting in the settings. Thats how 3 of my Redmi phones didn't have super annoying ad issues like TS.