I want to be able to play Kobolds and Catacombs again, or Battle the Lich King, but because I made a new account, I don’t have these.
You can purchase Wild Solo Adventures from the Blizzard Shop.
https://us.shop.battle.net/en-us/family/hearthstone#wild-only
You can claim the Kobolds and Catacombs and Knights of the Frozen Throne adventure for free from the following URLs.
https://us.shop.battle.net/en-us/product/hearthstone-kobolds-and-catacombs-adventure
https://us.shop.battle.net/en-us/product/hearthstone-knights-of-the-frozen-throne-adventure
Note that cards earned from these Adventures can only be used in Wild decks.