The data sheet should be authoritative provided you identify the part/die in use.
Pins may ultimately limit usability for certain applications.
You can use TIM that don't actually escape to pins for you're own timing purposes.
You can also use SysTick and schedule things
Each TIM has a single counting element, and usually 4 or 2 channels.
2 Channels CH1/CH2 are used for Encoder mode.
The F1 only has 16-bit TIM so no better choices.
One TIM can drive 4 channels at the SAME frequency, ie SERVOs at 50 Hz / 20 ms
The angle being driven by the CCRx registers. If you divide the counter to 1 MHz (via PSC) you can use the CCR as 16-bit microsecond values for angle, notionally 1000-2000 (1-2ms) with 1500 as a top-center. You could get more resolution, but doubtful that its helpful.
Data Sheet, and my math says 14..
https://www.st.com/resource/en/datasheet/stm32f103rg.pdf
