At least not yet.
The Elder Scrolls VI

Tim Stuart, Xbox chief financial officer at Microsoft, says that they will not make Bethesda titles exclusive to the Xbox platform, at least not yet. Stuart was speaking at the Jefferies Interactive Entertainment conference when he made these remarks, a full transcript of which you can find at Seeking Alpha.

Stuart was asked if Xbox planned to make Bethesda games exclusive to the Xbox and PC platforms going forward. Stuart says that Microsoft has no intentions of "pulling all of Bethesda content out of Sony or Nintendo or otherwise."

"We highly encourage cross-platform play, simply from this landscape of, if it's good for the gaming ecosystem, it's good for us, classic rising tide lifts all boats," Stuart said. Instead, Microsoft's plan is to offer the best possible experience with a Bethesda game on its own platforms.

"What we want is we want that content, in the long run, to be either first or better or best or pick your differentiated experience, on our platforms. We will want Bethesda content to show up the best as—on our platforms. [...] If you think about something like Game Pass, if it shows up best in Game Pass, that's what we want to see, and we want to drive our Game Pass subscriber base through that Bethesda pipeline.

"In the past, Bethesda was a little bit of a different lens to what we've done in the past, whether it's Ninja Theory or Obsidian or inXile, some of the smaller studios that had great IP. Bethesda gave us a great sort of launch with—I'll say, launch into a big, let's call it, group of content, a big catalog of content that we can use for Game Pass.

"When we think about Bethesda, it's going to be the continuing to allow—I'll say allow, but continue to sell their games on the platforms that they exist today, and we'll determine what that looks over time and will change over time. I'm not making any announcements about exclusivity or something like that. But that model will change."
Stuart continues on to say that they are continuing the hunt for other studios that they may want to acquire in the future. This echoes similar remarks from Xbox's Phil Spencer made over the past few weeks.

"We will continue to be acquisitive. We'll continue to look around the industry to find who has the great IP, who are great leaders, who has great product development, who can we rely on and say, we need a AAA game launching in FY '24 Q1 for Game Pass."