Is there any deck that can be built with only BotS or the last 2-3 sets? Preferably ~30k
Can't give exact values but for BotS exclusive option I'd say Swordcraft Aggro is your best bet. Mine is a mix of what I have but there's enough in the recent sets alongside classic/base cards to play a consistent aggro deck and BotS gives you Tycoon which I find quite underrated when it allows you to play out your hand so aggressively without running out of gas. Saves you the embarrassment of not being able to finish them and then just auto-losing.
Old Blood King, as mentioned, is another option. I don't have it as my Bloodcraft deck is a kind of janky Vengeance strategy but I've played against the budget version and it seems pretty good.
My Lion Crystal deck is unfinished but I have mixed feelings about that one; it can go really well if you do get a Temple going with your Lion's, but as a slower deck I feel you're risking a lot compared to other budget decks that have higher tempo. It's very hard to make cheap grindy or control decks that are able to compete, as expensive decks will crush with multiple win conditions or broken synergies etc.
The bright side is that the package are all bronze/silver and the burn and ward Lion-givers are good value cards so you can build around the theme without it being your only strategy. That and Haven has cheap removal which is never bad.
Only other thing I can think of is Runecraft Spellbook thanks to Truth's Adjudication. Obviously a lot better if you can get Giant Chimera but there's still a majority of cheap cards and the deck is playable as a budget variant.