A lot of audio ad broadcast software uses a combination of audible or inaudible tones to act as "triggers" to mark a location where an ad can be injected using some kind of location/time/etc aware data, the ad itself is very rarely baked into the stream unless it is something you're listening to a host read themselves.

In podcasts, the ad injection software will often pause the audio at the point where the ad tone occurred while it plays the ad, and resume it afterwards for continuity.

AdSwizz's AIS suite is one example of the tools commonly used for this: https://www.adswizz.com/ad-insertion-suite/

(I work in the internet radio space, lots of old-school internet radio streams are similar).

I also did hear American ads when listening to a foreign podcast in a non-English language.

It seems like the ads are added to the audio file at the start and the end of the podcast.

(I use Player FM)

I've seen this too. A politics podcast I listen to on Spotify played me some targeted get-out-the-vote messaging about my local & state races in November. I'm assuming Spotify provides them that data via customer's billing addresses. Or maybe they get it from location sharing via Waze (which has Spotify integration).

An MP3 files is mostly a collection of encoded frames. You can just concatenate them.