I saw there are many questions on this subject, but they don't really solve my doubt. Reading "Tensor Calculus for Physics" there is a point (chapter $3.5$) where it says that we can define $\widetilde{A} = \widetilde{A}_r\hat{r}+\widetilde{A}_\theta\hat{\theta}+\widetilde{A}_\phi\hat{\phi}$, where the component $\widetilde{A}_r,...$ represent the coefficient of each versor. Then after saying some things it states that $\widetilde{A}\cdot\widetilde{B}=\sum\limits_{\mu\nu} g_{\mu\nu}A^\mu B^\nu=\widetilde{A}_1\widetilde{B}_1+\widetilde{A}_2\widetilde{B}_2+\widetilde{A}_3\widetilde{B}_3$.
That in spherical coordinates it translate to $\widetilde{A}\cdot\widetilde{B}=\widetilde{A}_r\widetilde{B}_r+\widetilde{A}_\theta\widetilde{B}_\theta+\widetilde{A}_\phi\widetilde{B}_\phi$.
But this is not correct since this doesn't work for spherical coordinates. I saw in many questions that the usual answer rely on converting back to cartesian coordinates in some way. My question is how can we make this thing work in general in spherical coordinates without going back to the simple cartesian projections? Isn't there a way to fix it since it must somehow work in general coordinate systems?