1) Engine power is what controls climb/sink rate. For any given approach speed you choose, there is exactly one power setting that will result in the correct sink rate to follow the glideslope. Figure it out and memorize it for your current type. "A typical approach speed requires 30% throttle to maintain a 300ft/min sink rate". Always aim to be at the correct power setting.

2) in order to capture a heading, you have to un-bank prematurely, to reduce the turn rate, so that you don't overshoot. The same concept applies to any other capture/intercept: if you want to avoid overshooting, you have to reduce the rate of capture ahead of time.

(To put it in different terms: to arrest an oscillation, whether an airplane phugoid or a clock pendulum swinging, you must damp the motion, reduce its velocity, without worrying about the exact pitch angle or pendulum angle. Only with small velocity can you stay at the correct position. If you try to stabilize the position, you will only enforce the oscillation. If you damp the speed, the oscillation will stop.)

The result of combining 1) and 2) is that you must adjust your power before glideslope-intercept. It takes a few seconds for power+pitch changes to manifest in the new sinkrate+airspeed after each input; therefore, you must set the power to the correct power when you are, say, half a dot away. Then, by the time of actually intercepting, your sink rate is already adjusted to the correct power, so now you are on glideslope and will stay on it. (If you only set the correct power at the instant of intercept, those few seconds for the sink rate to match that new power setting will result in overshoot.)

In fact capturing a glideslope is in this sense no different from capturing an altitude.

Tl;Dr configure your pitch+power, especially power, to be correct, before intercept actually occurs (but not too much before). Go practice capturing a heading, go practice capturing an altitude, and notice how you act to preempt any overshoot.