The DisplayPort version itself specifies the maximum available bandwidth into which the combination of image resolution, refresh rate, compression and colour space, combined together, must fit. The refresh rate is therefore only one factor of many.

According to https://www.cablematters.com/Blog..., DP v1.4 (which is what this switch offers) can certainly do 1440p at 144Hz, but not quite 4K. 4K is only possibly possible if you restrict the compression (display stream compression (DSC)) and/or the colour space more (chroma subsampling (typically 4:2:2)).

Remember that all cables must also be designed for the desired DisplayPort version so that each component supports the desired bandwidth.