It appears that your scenario is based on the premise of the first definition. You're increasing speed while maintaining altitude, (intentionally) so the trim required is forward. (Faster speed = forward elevator and/or forward trim) But the STS, sensing that you're faster than original, trims aft in an attempt to slow you down to the original speed. This causes the plane to tend to climb which annoys you. (Of course, we're used to the premise of maintaining altitude) But this is where the engineering definition kicks in and you have to realize that the airplane doesn't care about the climbing tendency. It only wants to return to the original speed, which, being slower than the new speed, mandates a climb. This is the behavior of a normal airplane, only a little stronger with the augmented speed stability of STS. Understanding that (non-Airbus) airplanes really behave in accordance with the engineering (#2) definition, will hopefully let you come to terms with the "opposite" behavior
Not maintaining altitude, just a normal take off and acceleration. The STS is not supposed to do anything past 10 seconds after take off, but it does. If I follow your logic, it would trim towards the speed I had at lift off. It doesn’t make sense. Nothing with this system does.
If STS was completely disabled during take off, nobody would notice. When it works it tries to bring the aircraft into a stall.