For rate rises that are enacted to slow inflation (which slows stock market growth as you said) i think you have the cause and effect reversed.
The best way to see how inflation and stocks are linked is to look at economies where inflation is not intentionally slowed by rate rises. The stocks go up more or less with inflation (and some small % of gains they may have on top as you say). When you have rate rises that slow inflation you do indeed slow stock growth. But this is also inline with the link between inflation and stock price.
The best way to see how inflation and stocks are linked is to look at economies where inflation is not intentionally slowed by rate rises. The stocks go up more or less with inflation (and some small % of gains they may have on top as you say). When you have rate rises that slow inflation you do indeed slow stock growth. But this is also inline with the link between inflation and stock price.