New soldering iron smokes from inside the handle (not from tip) - is this a problem?
Maybe

I bought one of those from Maplin a year or so ago.  It produced a lot of acrid smoke the first time I turned it on, and I was also concerned about it. It's a very cheap and nasty product.

I dismantled it insofar as was practical, but couldn't see anything wrong with the wiring, but there was some residue on the hot parts which was burning off.  I put it back together, plugged it into a RCBO  protected extension lead, and left it turned on sitting on a fireproof mat in the garden for a while.  The smoke died away in a few minutes, and the smell was gone after an hour. The iron has been perfectly serviceable ever since.

Now, I haven't seen your iron, so I can't say for sure whether it's the same. Can you safely leave it somewhere for the smoke to die away? Somewhere fireproof, just in case.