It does sound as if the diagnostic pathway is underway, and I would not be too concerned about things like the teacher not knowing who is coming in to see him.
I teach and regularly get messages from the office that someone has left a message on the answering machine that they're 'coming in to see X' but didn't say where they were coming from! If they leave a number, we ring back of course but then they don't return our calls. Services are stretched very thinly at the moment. The important thing is that you received some feedback after they came in?
I will also defend their use of a single-seat desk for your son. Children have had to sit in rows this year, on desks for two. If your son sprawls, stims or cannot focus with another child next to him, it may have been the best way to support his regulation and the other children's learning.
But there are red flags in your post that I can't defend and I too would be looking for another school. The negativity in the report is unconscionable. A TA isn't always necessary to effectively support a SEN child, but if he is struggling as much as the report suggests, then why doesn't he have access to a TA? Covid and self-isolation policies may have stretched staff thin this year but what is the plan going forward?
Certainly, it does sound as if he needs support to develop and maintain relationships with his peers. Whilst school can't manufacture true friendship, there are effective interventions to promote social interaction and sitting him separate to his friends at lunch-time is the opposite of that.
If he eats very slowly could he sit with his friends until they finish, and then move to the table for slow eaters? Or do covid hygiene policies prevent this movement?
The thing is that there could be good justifications for all of their decisions but they should be communicating with you, not ignoring your emails and exacerbating your worries.
I would make an appointment with the SENCO and go with a list of questions.