STM32 RTC from battery
The reverse leakage current of your Schottky diodes is much, much greater than the current required by the RTC in the STM32. The worst case current required by the STM32 is \$2.2\,\mu\text{A}\$, but the worst case reverse leakage current of the diodes is specified to be as much as \$15000\,\mu\text{A}\$ at full reverse voltage and high temperature. Even if we look at Figure 4 for the behavior with a reverse voltage of \$3.3\,\text{V}\$ the leakage current looks like about \$50\,\mu\text{A}\$.

There is a reason why that pin on the processor is called \$V_{BAT}\$ and not \$V_{CAP}\$.