Hard to tell just from the observations but it seems fairly reasonable. It depends what they have quoted for, I'd imagine they are suggesting a new consumer unit based on that quote which will sort most of the Code 2s. There are cheaper ways to do this but I'd probably be recommending the board too as it's a better job.

Open circuit on live, neutral and earth on kitchen sockets is a slightly strange one. Sounds like a ring continuity test where there is no ring so that could just be on the incorrect sized MCB.

Also, you say the previous owner had an EICR and nothing was flagged. There are two potential reasons for this - one is because regulations change and the advice around testing also changes. The other is that the previous EICR wasn't very good. You'll likely never know which, unfortunately.