Roku is clearly doing paid placements for the device level search. It pretty obviously shows you "hey this is available here for $xx.xx" There's no confusion around when you're doing one versus the other. The device level search kicks you out of whatever app you're in and does the search from the dashboard.
As another point, I would never expect a search within YouTube to show results on YTM or YTTV. The roku just doesn't work that way.
The Search service is and has always been global.
And _Google_ wanted to inject results from another source (YouTube Music) when you searched (globally) with YouTube TV as the active app (which is not the same as YouTube search, which Google controls and can manipulate however they like), and filter other things out.
Your interpretation is quite misleading.
That's really hard to say: in its dueling email to its customers, Youtube TV says it was offering to continue the service under the old terms but Roku declined. These "carrier" disagreements generate more smoke and heat than light - with both sides blaming the other with carefully crafted PR messages that are technically true when you squint really hard: I don't doubt both statements by both Roku and Youtube TV are misleading in one way or the other (or have glaring omissions) - remember neither of them is under oath, they are just trying to sway public opinion. Don't put too much stock on what's basically corporate trash-talk on the side-lines of negotiations.