Don't overthink it too much. Simplify in your mind. Trim is used to pre-set hands-off angle of attack. Static stability forces will focus on regaining the trimmed angle of attack if the plane is displaced from its trim state.
Since pilots use airspeed as a proxy for angle of attack, trim sets hands-off airspeed, as far as the pilot is concerned. The best way to conceptualize trim in flying is to think of it as a hands-free speed setting dial.
If a plane is disturbed from trim, it will be disturbed from trimed AOA and ultimately speed, and its static stability creates restorative moments that pitch the plane in search of the original trim state. So if below trim speed/above trim AOA, the plane pitches down, and if above trim speed/below trim AOA, it pitches up.
So the thing to keep in mind is, if the plane is disturbed by a gust, and you make no changes to power or configuration, it will naturally seek to regain the AOA/Speed it was at before it was disturbed. You can let it go and hands-free, it will seek that trim state on its own, but will take its sweet time, and oscillate about the trim AOA in smaller and smaller excursions until back at trim AOA/speed.
Generally you don't want to wait that long, so it's more efficient to help the natural stability forces along, with elevator inputs, to short-circuit the oscillations. To do this effectively, you need a handy proxy for AOA that can be used, in the moment, as a target to shoot for with your elevator inputs. For this we use pitch attitude relative to the horizon.
So you are flying along nicely trimmed, the plane is flying along hands free minding its own business, pitch attitude set, and a something changes AOA and speed. Pitch attitude will also have changed. Your objective is to get the airplane back to its trimmed AOA/speed. Instead of letting it hunt up and down and eventually get back to its trimmed state, you make subtle elevator inputs to regain the original pitch attitude, thereby getting back to trim AOA as soon as possible. Once you have regained the original airspeed, the plane should be back to and holding the original pitch attitude, and you're back to where you started.
You should be in the habit of using trim to set a hands-free speed for the plane to fly for any stabilized speed you want to fly at (for more than, say, 30 seconds). If you want to fly at 70kts on approach, don't leave it trimmed at 90 kts and hold elevator pressure; trim away the pressure until it will fly at 70kts hands free. Same for any other speed condition that is more than a short-term transient condition; shoot for the target speed by pitching to a target pitch attitude, and when on-speed, trim away the stick forces so that speed is held hands-free. This is how to fly with minimum work load, by letting the plane's inherent stability do most of the work.