No, you can't obtain such information via API.
Information from description ( https://www.chess.com/news/view/published-data-api ):
The PubAPI is a read-only REST API that responds with JSON-LD data. Our goal is to re-package all currently public data from the website and make it available via the PubAPI. "Public Data" is information available to people who are not logged in, such as player data, game data, and club/tournament information.
Hi!
I just started playing chess. I noticed there are personalized training suggestions in the post game analysis (in the report tab)
This:

So I figured maybe I could collect the top X most common suggested trainings over Y time, and focus on the ones i get suggested the most.
I can get my games from the api. But I cannot find the training suggestions anywhere.
Is it possible?
Alternatively, could I fetch it from the web page itself somehow? Seeing as I have the game links from the api. But my webrequest/curl for that page url does not contain the word "training". So maybe I'm missing something