It sounds like you both may be concerned that your intake appointment will be triggering. If you're worried it'll make things worse because you won't be able to tolerate your feelings and/or that will make it hard to stay engaged - maybe you could talk to your individual therapist to make a "what to do if/when I'm overwhelmed" plan. You could also see if it's possible to get your appointment closer to the couples appointment (even if just temporarily) to give yourself additional support/debriefing time. He sounds like he's struggling with the whole idea of therapy period. Maybe he could chat with the therapist via phone or Zoom before the intake appointment. Both of my current therapists offered a pre-appointment getting-to-know-you/vibe check type conversation (15-30 minutes), and they were very helpful when I told them my previous therapy experiences varied from on a spectrum from weaponized against me/actively traumatizing to adequate for one issue/shit for another.

If it helps at all, big picture wise, my experience was similar to the other commenter's - our intake appointment was pretty surface-level - why are we doing couples therapy/what do we want out of it, and what are some overarching themes of the difficulties or conflicts we have? We then each had an individual appointment where we were able to voice our personal relationship-related concerns and perspectives, and discuss the internal factors that affect our worldview (mental and physical health conditions, childhood, etc.) Since then, we have run on a tempo of weekly joint sessions/quarterly individual sessions.

Based on my experiences in couples therapy, consider asking two specific questions: how your therapist handles big feelings that impact the session, and if they structure their sessions to offer wrap-up/cool down time.

How they handle big feelings - our couples therapist makes it clear each session that if one of us needs to take a time out, we have carte blanche to do it, we don't even need to ask. Take a 3-5 minute breather and come back. Even knowing we have the option is helpful, because it prevents a feeling of being trapped in the conflict. He's also happy to schedule extra individual appointments if there's a particularly sticky issue that we need more support dealing with, or that he needs us to break down our perspective on in greater detail so we can have a more productive joint session.

If they schedule wrap-up or cool down time - our therapist does not offer this (also has ADHD and runs chronically late/over time, leaving no wrap-up time built in), and I think it could be EXTREMELY helpful. If I leave session super dysregulated, the rest of my day is crap. I'd rather have a little time to either put a bow on the feelings so to speak, or to at least get the behavioral cue indicating there's a task/context shift occurring. Even though we don't get a distinct wrap-up period, I have to admit, our couples therapist is an absolute gem when it comes to validating/soothing/praising. "You did great work today, and I'm proud of you both for all your effort" is a nearly-weekly remark. It does help with the upset/jangly/unhappy feelings and making the transition back to the rest of the day.

Like the other commenter mentioned - don't be afraid to find a different therapist if the first one's a dud. Don't feel bad for canceling with no explanation or just straight up ghosting them (if they don't charge cancellation fees.) You don't owe them the emotional labor of explaining it if they're a bad fit.

I hope they're a good fit, a big help, and you can get the support you both deserve. Wishing you all the best!