Here are a couple of slides showing the relationship between CO2 and annual temperature anomalies from 1980 thru 2022 conditioned by the type of year (viz., el Nino, la Nina or neutral) as defined by NOAA.  I used an ANCOVA analysis in the "R" package "HH".  The first slide shows the summary results.  The key takeaway is that the relationship is statistically significant (F-test).  The second slide graphs temperature anomalies and CO2 levels with the type of year set as a "factor" in the ANCOVA analysis.  The key takeaway is that the slopes showing the underlying rise in temperature anomalies as CO2 levels rise are consistent.  What does change are the intercepts.  El Nino years see a jump in the intercept while la Nina years see a drop in the intercept relative to the neutral years.  In other words, the type of year (whether it's an el Nino or la Nina or neutral year) shifts the temperature anomaly up or down, but does not affect the slope.  The underlying slope of the temperature rise is a function of CO2 levels.