I think I noticed it widespread in the mid 2010s. Maybe around the same time that DIY and various hobby/handicrafts became just "making".
I still remember when I bought a tool off someone and was chatting about what i was going to do with it and they declared out of the blue: "I am a maker!". I just had to end the conversation as quickly and politely as possible. I don't know what the point of that statement was, but it made them sound a bit unhinged.
That said I'm sure the term coding was in use before, but more like a sub-activity that 'computer programmers' or 'software engineers' might do as part of their job. Maybe 'coder' and 'coding' became more popular with the spread of the term 'agile' into the bullshitting-consultant / middle-management cultures; I think that's when some people started using that term as an excuse for skipping 'design' and 'engineering' parts of any complex project.