I'm in the same situation as OP.
I wanted to try a segwit address to receive some funds from an exchange.
So I generated a new regular address (the old way) then I went to console and did command addwitnessaddress newaddress and got another address with starting with 3
Then, with the intent of confirming I own the keys, I tried dumprivkey on the new segwit address and got the same error as OP.
I would love some knowledge to weigh in on what I'm dealing with, at a practical level.
What exactly is this segwit address I have starting with 3, and why's there no privatekey to it?
What happens if I send funds to it? Is the balance held under the orig address?
What's the difference between this and the first non-segwit address?
Why should I use 1 over the other?
TIA!!