Here is a test that works 99% of the times: press the app switcher.
If it truly is in the launcher, then it should be empty. If it's not the launcher, it should focus the app that is causing it.
You can even double-confirm this if you can install a 2nd launcher, set THAT to default, but launch an app from the system built-in launcher. If it focuses to the system built-in launcher, then it is indeed what shows the ad.
Sadly there is also the Xiaomi case, where every system app has ads built in, but it's all managed by the app named "msa" (I assume it means "Mi System Ads"), and disabling that will get rid of all ads, unless it's a separate ad system baked into the app (afaik Music and Browser are such cases).
I'd look through the app list (there should be a menu where you can show all system apps), or even use an Intent explorer, like AnyCut (it has a mushroom logo that looks like it's from the Android 2 / Android 3 era, don't download the newer version, it's borderline malware as far as I remember), and see if there is any suspicious Intent in there that could hint towards.
tl;dr: it's *extremely* unlikely that the app trashes the launcher layout completely empty, and replaces it with the popup layout before launching an app. It's much more "Android-esque" that the popup would be an Intent that could be launched.
Note, that if you do find a suspicious Intent that may be responsible for the ad, don't try to launch it, it will most likely just crash due to missing Bundle parameters.