Brann bronzebeard not showing up in wild cards

The core cards that just rotated out are missing from my wild cards? Does this mean I have to get them again from packs? I’m confused regarding these rotations? How do I know if I have a card because I packed it or simply because it’s a core card? Thanks,

To illustrate how that works, let’s look at a card that is in the current Core set, but also part of a Wild set: Dragonbane.

When you look at your collection, you most likely see a normal and a golden version (unless you have not levelled up your Hunter class fully, in that case you’ll see only the standard version). These are both listed as being part of the Core set, and they are uncraftable. You will see these versions (and these versions only) regardless of whether you set the expansion filter to Standard Cards, Wild Cards, or Core.
These are yours for as long as Dragonbane remains in the Core set; if it is removed and replaced by another card in a future Core rotation, then these cards will be removed from your collection. Since you received them for free, nothing of value is taken from you when this happens. They simply replace a card for another card as Core changes.

But if you set your expansion filter to the correct expansion, in this case Dragons, you will see the copies you own from the Descent of Dragons set. In my case, I see only a normal version, because I do own this card as normal but not as golden. You might see both versions, none at all, or one of them.
These copies are craftable. You can, if you choose, disenchant them, or craft them if you want to own those copies. They are, however, never used - during this standard year. But if Dragonbane rotates out in a future Core refresh, then only the Core copies are removed; the Descent of Dragons versions that you own will remain yours. So if you play (or plan to play) wild format (including some Tavern Brawls) and want to be able to use Dragonbane even when it is no longer in Core, then I recommend NOT disenchanting these cards. Because if you do, you will have to re-craft them once it’s no longer a Core card.

If you had asked me this before the last Core refresh, then I could have typed the same answer using Brann Bronzebeard as an example. Instead that in that case, I would have told you to check the League of Explorers set for the original version of the card, rather than the Descent of Dragons set.

In the case of Brann Bronzebeard, you cannot earn him from packs. You can earn him by completing the second wing of the League of Explorers solo adventure.
If you have already completed that wing and don’t own a copy, then I assume that you have at one point in time decided to dust your original copy. Perhaps when it rotated to Wild. Perhaps when it “returned” as Core and you mistakenly thought that the League of Explorers version of the card was no longer needed. If this is the case, then the only way to get the card back is to re-craft it.