And then he's out until he's completely healed or woken up with the phrase, 'Wake up, Miles.'
He's put in the tank and left to float under Gelrath's enthusiastic supervision ("He's taking to it better than the projections estimated! He shouldn't be in there long at all!") with various monitoring equipment to make sure nothing's going to go horribly wrong.
Nothing goes horribly wrong.
Callida returns to handling various matters that are meant to be handled when one's in charge of a fleet and on a diplomatic mission on a foreign planet. She talks to people, she quietly looks for outlets to purchase various materials her fleet's projected to need, she starts attempting to learn English. Envee's attempts to figure out a system of data conversion march up the gentle slope of progress, until they can directly convert text formats. This isn't good enough for her, so she'll keep at it, but it does mean that Barrayar (and Cordelia) can have dossiers on some of the major planets in the Sith Empire's home galaxy. Everything that's sent is carefully edited by the fleet's (somewhat) pitiful Imperial Intelligence for anything that might be security relevant.
Dr. Gelrath finds not having appropriate medical terminology translated very annoying, and he has little to do while Miles floats unconscious in the tank. He wants, very badly, to exchange relevant medical information with all doctors ever. Callida - will allow this, though she will be monitoring him to make sure he doesn't say anything he's not supposed to. He happily shows relevant doctors how the kolto tank works (He asks for another one so he can demonstrably put other injured Barrayarans in; Callida says he can ask if he has any specific injured Barrayarans to put in a tank, but otherwise, he may not.) and how some of the less kolto-related equipment works, too. They're better at adapting to bizarre systems than native tech, and he starts requesting digital books for the doctors on the subject from Sith Imperial Intelligence. Sith Imperial Intelligence sighs heavily, checks everything over twice, has it approved by Callida, and grudgingly sends them where Dr. Gelrath wants them.
He persuades Envee to put her pet project down for a while to come translate for him, so he can be incredibly nerdy with more efficiency. Callida tentatively allows this, but mysteriously hovers nearby the protocol droid at all times while on the planet. Envee graciously puts up with the fascinated/horrified staring and awkward questions and the stammering with a grace usually reserved for trained diplomats. She answers appropriate questions with polite, phrased-for-Barrayaran-sensibility replies. She translates Dr. Gelrath's medical-themed technobabble with perfect acuity, and when she has free time she helps all Sith Imperials with English skills, including Callida.
Neither of them have much in the way of 'free time,' so these lessons tend to occur anytime and anywhere, when they're both free enough. In the groundcar, in hallways, in waiting rooms - nowhere is safe. Sith are notoriously difficult to ambush, but Envee tries her best. Callida finds this amusing, usually, and plays along with unexpected syntax lessons. She improves, slowly.
Dr. Gelrath's enthusiasm is - somewhat warranted. Through some combination of a healing trance and what the doctor describes as a 'beneficial cascading effect,' Miles is given a clean bill of health and taken out of the tank. Gelrath assures everyone that kolto's soporific effect is well documented and that Vorkosigan's continued sleep is totally normal, actually, here, have the documents, they can just transfer the data now! ... After Sith Imperial Intelligence checks it over. (They are growing to quietly despise him.) Everyone is assured that he'll wake up soon enough, and actually, while Gelrath's at it, who wants to learn about how to properly use kolto medicinally, he bets the Barrayarans do, can he teach a class on it, he's so excited, they can dump more Barrayarans into the tank as way of demonstration!
(No. No he may not. Kolto is still non-renewable. He may instead send her a request if he has a specific person to put in the tank, but he is not allowed to just dump anyone he wants into it.)
Callida quietly finds opportunity to check up on Miles's health now that he's out of the tank, since she can detect things both sets of technology can't. From what she can tell, he's absolutely fine, the healing trance should end soon enough.
This is where her latest English ambush takes place.
"I'm better at reading it than speaking it," sighs Lord Callida in Basic, after failing to conjugate a verb correctly. "Or listening to it spoken."
"You've got more practice with dead languages than living ones," says Envee, in English. "Your comprehension's good, but it's going to take time for you to be good at putting your own sentences together, that's just to be expected. Complain at me in English."
There's a long pause as Callida tries to draft something that makes sense with her incomplete vocabulary.
"Stop worrying about getting it perfect. It's just me. Say things, mess up, figure out what you did wrong so you can do it better. Otherwise you'll just hover noncommittally forever, trying to make the perfect sentence, and never get any actual practice speaking."
The Sith Lord sighs. But she switches to English, and haltingly says, "It is - easier to understand. Than to speak."
"See!"
"No, listen," corrects Callida, dryly. In English.
And that causes Envee to get distracted snickering.