This is a gross over simplification. You make it sounds like mining farms are using the same equipment for 4 years, and then as soon as the halving happens, they all change en masse to some new equipment, which is obviously nonsense. All mining farms will be gradually upgrading or replacing their mining equipment over time depending on equipment costs, electricity costs, profits, the age of their old equipment, as and when it breaksdown or becomes too costly to repair and so on.

There is no "new algorithm challenge". All that happens is they earn less in the way of a block reward. The mining process is identical, and all equipment currently mining bitcoin will still be mining bitcoin after the halving.