I am looking for examples of finite-dimensional commutative $\mathbb{C}$-algebra $R$ with an ideal $I$ such that $$R/I\otimes_R I=\{0\}$$ and an $R$-module extension $M$ "the-other-way-around": $$0\to R/I\to M\to I \to 0 $$ which has the exact opposite vanishing tensor products and acts as "second identity" as follows: $$M\otimes_R M=M $$ $$M\otimes_R R/I=\{0\}$$ $$M\otimes_R I= M$$ $$I\otimes_R I=M$$ The question might become trivial from certain perspectives, but I would be very happy if you can provide such an example or indicate how to construct a family. Any hints how these conditions appear in literature are also very welcome. Or I am also happy if you can explain to me why this is impossible (then my next question would be using bimodules over non-commutative algebras...)

Thanx very much for your help in advance!