While the timing does feel suspicious, it's pretty unlikely that it was an implicit or explicit part of the settlement. According to NYT it's been losing money for years, despite having good ratings:

“The Late Show,” a fixture of the network for over three decades, was racking up losses of tens of millions of dollars a year, and the gap was growing fast, according to two people familiar with the show’s finances.

...

“The Late Show” began losing money at least three years ago, two people familiar with the finances said.

While sometimes losses make sense in business (eg Costco's $1.50 hot dogs), I doubt this was one of those cases. I personally think the cancellation was a separate decision, though still related to the Skydance acquisition, because they probably wanted to cut unprofitable shows in order to improve their valuation.

I think the bigger issue is that it's so believable that this could have been a quid pro quo! When you pay $16 million to settle a meritless lawsuit with the president as a bribe so your business deal goes through... you've lost all credibility. You're shown you're willing to bend the knee to the self-appointed "king".