IMO, a NAS should outperform Tidal depending on the quality of the drive you are using for the NAS.
One of the reasons you want a server is to tame the extremely volatile internet. If you are just using a streamer, it has to work harder to settle things down. A high powered server is best sending the signal to a lower powered player. I have never heard a streamer perform as well as a comparably priced server and renderer.
If your NAS is SSD based and is quiet and fast it should outperform Tidal sending a signal to a streamer. This assumes it is on a wired connection, etc... But, the key is quiet and fast. As pointed out above, noise can come from a lot of places and the goal is to minimize this.
If your local files are underperforming compared to Tidal then you have an issue on your network. Local files should outperform tidal.
Regarding which is most important, DAC, player, server, cables I agree again with the above that it is all important. Given that there is less deviation in tonal profile from servers/renderers vs DACs, I think you start with the DAC first as it can be more colored. And then pick the optimal device for your DAC choice.