When the colonists hack into the communications channel, it's suggested it's easier to do so because it's holo-tech communications. It has a bigger data bandwith and the security is lower and plain 2D comms are more secure - they can have higher encryption protocol without significantly increasing the size of the message. Mack has suggested that this will become the reason why holo-comms are relatively abandoned.
I think it probably would have been better served to not make any explicit mention of the aesthetic differences in the set design or the uniforms, and let readers pick what they want to picture (TOS, Abramsverse, or Discovery).
The whole hologram/viewscreen difference was completely glossed over, as far as I could tell. You get cuts between Pike being a hologram on the Shenzhou and the entire Shenzhou bridge being on the Enterprise's viewscreen, without any explanation for the discrepancy. (And if I missed one, please let me know!)