Check the video you published in the sensitive data and pay attention between the first click and the second. The first is slower. You, having a fast PC, notice the slowness less but it is also yours.
As you point out yourself in the sensitive data, the first click takes almost two rotations and the second one rotation. instead the second click is instant. One rotation of the icon should equal one second. A second of reactivity is slow, imagine that I have 4 rotations because I have a slow mac.
I removed the code added by my colleague and disabled our plugin to check the reply feature. It still behaves similarly as it does with our plugin enabled. The first time it takes time and the second time it works quicker. So it isn’t related to our plugin or happening because of it. Here is a screencast: https://i.rankmath.com/9YG8VM
This is related to browsers as they cache the pages and load them quickly on the second load.
Hope this helps. Let us know if you need any other assistance.