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Update:

I also looked at the output of fa_results$loadings in both cases. It displays not the same summary values for varimax as print(fa_results) but the output deviates in the case of oblimin rotation to a greater extent. Which values are the correct ones?

Oblimin: Deviation in comparison to print(fa_results)

Oblimin Rotation:
>fa_results$loadings
[...]
                 MR1   MR3   MR5   MR2   MR4
SS loadings    2.310 1.350 0.975 1.038 0.563
Proportion Var 0.257 0.150 0.108 0.115 0.063
Cumulative Var 0.257 0.407 0.515 0.630 0.693

Varimax: Deviation in comparison to print(fa_results).

Varimax Rotation:
>fa_results$loadings
[...]
                 MR1   MR3   MR2   MR5   MR4
SS loadings    2.444 1.450 1.064 0.913 0.806
Proportion Var 0.272 0.161 0.118 0.101 0.090
Cumulative Var 0.272 0.433 0.551 0.652 0.742

The mean communalities amount: 0.7418824 The summary table also report the 0.74 as the explained variance for the oblimin rotation:

The mean communalities amount: 0.7418824 The summary table also reports the 0.74 as the explained variance for the oblimin rotation: