I don't understand how the power of compounding would work in stocks. Or does it only apply in places where you gain interest and re-invest it?

You need to understand the rational behind stocks and shares and dividends. We could look at it in this way.

1) company stocks are the "fair market value". If a business do well, it appreciates in value e.g 5% increase in stock value. Next year, if business does even better, the "fair market value" increases, but maybe only at 4%. So total gains of 9.2% of 2 years ago. We term this at capital appreciation. This is your compounding interest in play (in terms of stock value).

2) stock is more complex because the value is derived from market value and business. Business can fail, so stock price can fall. Hence its is more riskier than just compounding interest from savings account. (since savings accounts are from banks mostly go to loans).

I hope this gives a much clearer or alternative picture to look at stocks and shares.

Buy an ETF that automatically reinvests the dividends such as IWDA or EIMI.