Many people seem to believe that their phone is always listening and serving them targeted ads related to things they've said. Will convincing evidence come to light that this was actually happening on either iOS or Android?

This would have to be on either an OS level, or on enough common apps (particularly if they could record when not in the foreground) to substantially justify this belief. State surveillance, targeted exploits, or a couple of rogue known-to-be-shady apps (eg TikTok) would not resolve YES.