Can someone help me understand inflation, supply chains, and interest rates?

Greetings!

I am trying to understand what is going on right now regarding inflation. My knowledge is very limited, but here is what I think I understand as of now.

When the pandemic started, the Fed lowered the interest rates to stimulate the economy and avoid a recession. During the pandemic, disruption of supply chains coupled with high demand (since we managed to avoid a recession) caused an inflation surge. In order to slow inflation, the Fed should raise interest rates, but that could disrupt the stock markets.

This is where it gets mushy in my head. Why would higher interest rates slow inflation, and why could they disrupt the stock markets? How exactly are all these concepts tied together, and how do we move forward?

Thank you for your help!