Picking up a profession you previously abandoned won’t bring back recipes or skill levels, you would be starting again from scratch and have to level up each expansions skill and recipes list again.
There is one exception for this, as Legion recipes for the most part were part of the quest chains and given as rewards, you can’t repeat those quests.
So there are items for each profession in Legion that will give you back the quest reward recipes.
For Blacksmithing that would be Forgotten Plans of the Broken Isles
That will only give you a way to get back Legion recipes that were quest rewards for quest you’ve already completed on this character though.
Higher ranks from world quests etc would not come back and you’d need to recollect those after relearning the Rank1 version.
For any other expansions recipes, you’d want to visit the trainers, discover from crafting, hunt for drops etc just like you did the first time around to collect those again.
Hope this helps 