Or is it dependent on how many I have already drawn or played during my turn?
A: Rules take effect immediately, and the wording on Draw/Play Rules states that you should “Draw/Play [x] cards per turn.” Therefore, if you have already played 3 cards on your turn so far, and the rule is (now) Play 4, then you can only play one more card. The count does not start from the point the card is played, since the number of cards played is per complete turn.
Here’s another example which may be useful: If “Play All” is in effect and you play 6 cards, and then play the card “Play 3,” your turn simply ends, since you have already played 3 and have no more remaining plays in your turn.
Draw rules are similar, in that you count the total number you have drawn on your turn, so if you start with “Draw 3” and then play the card “Draw 4” you only get to draw one additional card, since Draw rules specify “so that you have drawn [x] cards on your turn.” When you increase the Draw rule, you only draw the difference. If you decrease it on your turn, however, you don’t have to “Un-draw.” You just get to keep the excess cards you drew when the Draw rule was higher.