Yeah. We seem to be on the same page, so I won't talk your ear off about it.

[And just telling Byleth to trust and confide in him, when Claude had built up a solid reputation of being untrustworthy and deceptive... Well. That definitely wasn't going to happen overnight. But a friendship can't be built if he doesn't extend a hand at all, and Byleth certainly could use it right now.

He draws his cloak closer around his shoulders, and leads the way once more. By the time he takes them to a winding side alley and a gate leading into a shaded, leafy courtyard, he's trying not to make it obvious that he's shivering. But once they're inside, it becomes more obvious why he brought Byleth here, of all places: closing the gate behind them, the noise of the city seems to melt away. There's a star-shaped fountain in the middle of the courtyard with flowers scattered across the surface for decoration, and warm lamps to light the way into the teahouse.]

Here's the place, just through the doors ahead. I found it a few weeks ago.