Using the TV AI Explorer, it is possible to search the OCR'd onscreen text of BBC, CNN, MSNBC and Fox News from January 1, 2020 to present, with a 24-48 hour delay. Searching for appearances of Donald Trump's social media handle "@realDonaldTrump" in the onscreen text makes it possible to track citations of his social media posts on television news, offering a rough proxy of the degree to which his posts are directly driving the news cycle.
Matches include tweets, Instagram and Facebook posts and even displays of his handle on campaign backdrops, but overall offers a rough approximation of the prominence of his social content in the news.