Isn't the solution in game theory when there are multiple turns to just repeat the move the previous person made.

So if the other side overpumped by x1 amount then you pump an extra x1 the next turn / year (maybe multiplied some reference production factor as they don't all have the same absolute limits).

Simple game theory doesn't work in the real world. In the short term most OPEC+ members other than Saudi Arabia have very limited technical ability to significantly increase or decrease production. It's not like they have a big valve that they can open or close at will. For many oil wells, restricting flow would actually damage the geologic substrate. And drilling new wells (including all of the supporting infrastructure) can take years.

Tit for tat (start by cooperating, and for each subsequent choice do what your opponent did last turn) is the optimal for repeated 2-party prisoners' dilemma.

The real world is much more complex. OPEC is a multi-party game, for starters. For another thing, there are cascades of social/political problems that get in the way of optimal strategy at the level of nations. I.e. that only works if politicians are more interested in solving problems than controlling narratives or maintaining power. Unfortunately, an ineffective leader can be sustained by controlling the narrative, while an effective leader can be destroyed by lack of control over the narrative. And one of the best ways to control a narrative (especially if you aren't a very good leader to begin with) is to create so much chaos that it distracts from your shortcomings, and blame the chaos on enemies.

Not always. In a simple game yes, but sometimes the game is more complex and so it is to your advantage to play even when you know others will defect.

Then they all pump more every year