OK, here’s the skinny: At 30 fps second (frames per second) 1 second of animation requires 30 frames rendered. So, if the same action is to now last 2 seconds, it will need 60 frames rendered (60 frames/30fps = 2 seconds animation length). You can do this by scaling all the animation keys along the X-axis (time) in the Dope Sheet or Graph Editor, or by setting the Time Remapping option to 100 Old, 200 New. This last option can be confusing because of the way it changes how the Timeline works, but can also be very accurate and simpler than scaling.
Yes, reducing the fps for playback will slow the animation but also amplify any problems with strobing and stuttering, and is not a good choice for slowing things down.
Just as an example, in film cinematography, 24fps is the standard and cameras take (expose) 24 still frames per second. Most can be “overcranked” up to around 48fps (slowing the action by a factor of 2), but for the real slomo stuff, specialized high-speed cameras are used that can take thousands of frames per second. With these specialized instruments, actions like a bullet bursting a balloon, that happen in less than the blink of an eye, can be filmed so the same action lasts 30 seconds or so. But instead of taking a couple of frames @ 24fps, the high-speed cameras take thousands. By the same token, you need to increase the number of frames rendered for any particular action.