Competitive coding, despite superficially involving typing code into an editor, has almost nothing to do with working on large pieces of software. It's a lot of rote memorisation, learning algorithms, matching them onto very particular problems, and so on, it's more of a sport. Just like playing too much bullet chess can be bad for your classical chess I can honestly see how it gets into the way of collaborative work.
If you already know that there is a tactic in the position your entire frame of reference changes. Which is actually why puzzle composition is treated very differently from actually playing, and a lot of famous composers are not particularly strong players.
This is why I feel it compares well to coding competitions. It looks so similar, but the mindset is very different. And only looking at tactics, just like only looking at coding as a game problem is I think why it may damage your performance at work.
"Chess problem" is a term of art that refers to an artificial composed position with a unique solution that is constructed to both be a challenge to the solver and have aesthetic value. They often have constraints on the solution such as that White must deliver checkmate in two moves (three ply). This is what I assume you're referring to.
A position from an actual game (or that easily could have been) that demonstrates a tactic (or combination of them) is generally known as a "chess puzzle", largely because the term "chess problem" was already squatted on.
Somewhere in between the two is the "study", which is a constructed position, less artificial than a chess problem but still very carefully made to have a unique solution that walks a tightrope and generally requires absolutely exact calculation rather than working by general tactical principles.