Sometimes having a diagnosis provides the key, and sometimes it's at least as useful to focus on what the difficulty with functioning is, and then figuring out how to help so it's not so difficult. I will take the latter approach with my answer.
I remember when my children were in kindergarten, one of the topics in the curriculum was feelings -- acknowledging, recognizing and naming them. That suggests to me that children don't always find this a breeze. Also note that my spouse is pretty awkward socially but is very smart, and I've noticed that that combination is not unusual. And as my mother used to say, "You can't have everything and curly hair too." That's my paragraph on reassurance.
I have some suggestions for the what to do about it.
It sounds like you've made some good observations about what questions cause difficulty. So, you could read What Do You Say, Dear? by Joslin together, and then (again, together) gradually add some pages (based on your observations), such as: What do you say when someone asks you, "How's it going?", and then brainstorm possible formulaic responses, e.g. "Good. You?" If your child has trouble proposing possible responses, you could provide several options for him to choose from, to add to the book.
When your child gets a little stuck in conversations, when you are around, you can assist, e.g.
(a) Let's say the question is "Are you tired of Zoom for school?", and you happen to know that your child IS tired of Zoom, or actually likes Zoom, you could turn to your child, and ask a confirmation question, e.g. "You're pretty tired of Zoom, right?" or "You actually kind of like Zoom, right?"
(b) Repeat the question, rewording it as needed.
(c) Or you could provide two or three possible options, e.g., "Are you tired of doing school over Zoom, or do you like doing school over Zoom?"
The reason a, b and c can be helpful is that your child is more accustomed to responding to you than to others that he doesn't know well. Also, he is likely to be more relaxed and less anxious when responding to a question from you.
Roleplay with favorite stuffed animals.
Make some simple Readers Theatre scripts that you can read and act out together. I like to make these with quarter-sheets, stapled down one side, with text on one side of the paper only. This makes a little booklet that it's easy to carry around as you're acting things out.
Model sharing feelings of awkwardness when your child is observing you interacting with others, and tell someone close to you, in your son's hearing, that you felt awkward in a certain situation, and weren't sure what to say. This could be in person or over the phone. Make sure you pretend that you're not aware he's listening or might be listening. (This is a good trick for sneaking in some positive feedback about the child, too!)
If a child freezes up and then starts feeling anxious about freezing up, that can make things so much worse. So, the idea is to normalize the feeling, to help him relax about it.
If you decide to discuss your concern with a doctor or therapist, I suggest you initiate the conversation out of your child's hearing. You could perhaps use the patient portal, email or phone call initially. What I did, for our initial evaluation for Tourette Syndrome was, I had my spouse come along and play with my son in the waiting room while I had a short initial conversation with the pediatrician. I asked the receptionist beforehand if we could set it up that way. This was quite helpful. It's so helpful when we as parents can project a low-anxiety attitude towards our child, so as not to amplify any concerns the child may be having about himself.