Its the end of an xpac, population will be at an all time low until pre-patch hits, so it will look dead in spots all over the game.
The only thing that the server has an effect on is Auction House (which is cross faction), guild membership, and the amount of characters you can trade non BoA amongst/have in the same guild. To clarify the last two points; for example, on a two linked servers, like I am on (Alleria-Khadgar), between them you have 28 slots to create characters on, that can all mail each other gold/items/ect. You can also have the same name, just with different servers, in the same guild, like Burns-Alleria and Burns-Khadgar.
Legion seemed to have limited CRZ on release, in that, on a few of the hidden mount hunts you could jump to a dead server cluster and usually get items you needed. Now, from my understanding, all content going forward is completely CRZ, exspecialy considering how they are billing Warmode sharding tech, and the aim for it to be balanced.
With the introduction of WoW communities/cross realm chat/BlizDiscord, even guilds are almost meaningless, unless you raid mythic or like to buy carries.
So, if you use the AH a lot, like to spout political tolling bullshit in trade chat, or run mythic, servers might be important, otherwise, it wont matter in BFA.