Another NOOB question

I am trying to plan my pin usage for my project with future additions in mind so am trying to understand what resources I2C requires.
I am using my STM32F401CCU6 Black Pill which seems to have 3 I2C ports.
As I am using a number of encoders and have a PWM output, I want to make sure that I leave myself open to adding an I2C interfaced LCD or OLED display later.
So the question is: Does I2C use the timers associated with the specific pins?
ie. If I select to use the second I2C interface:
on PB3 - SDA2 is associated with Timer2 Chan2
on PB10 - SCL2 is associated with Timer2Chan3
This would lead me to believe that I should not use Timer 2 for any other purpose? (PWM and/or encoders)
Then in the case of the 3rd I2C:
SDA3 is on Tim3Ch1
SCL3 is on Tim1Ch1
This is split over 2 timers???
Do I need to take the SMBA channels/timers into account?
PB12 - SMBA2 is on Tim1_BKIN
PS. The only reason I have not mentioned the first I2C interface is because I have used Timer4 for 2 of my encoders. As I am already using all of my ADC pins, the only other place I could put these encoders would be on Timer 1, but am not clear on how wise this would be? ie. Is there anything special about the advanced control timer that would give me pause on using it for reading my encoders?