If you have any items you are especially concerned about, make sure they are account bound and you know which battle.net account you are using now.
But transferring servers, people do it literally all the time and you can buy 8 packs from Blizzard. The realm servers don’t have much relevance anymore. You are moved into a new shard dozens of times a day when playing.
Blizzard sometimes has to do weird things in classic when you clone a character and there’s room to miss some deadlines they have for a new season, but this also seems far removed from the concern.
TLDR; servers are safe to move across but moving characters between accounts should have some consideration.