I was surprised to see this Tumblr post describe ～んだった used to mark regret. I can only assume it's true, but I'm not sure (1) how much of a colloquial expression/slang is it? (2) what does it come from, grammatically?
I'm familiar with のだ → んだ, but that doesn't seem like the past form (past+んだ) so is it maybe some kind of abbreviation of んだったらいい？ It doesn't really make sense though... and I couldn't really find anything anywhere else!
According to 明鏡国語辞典:
の-だ〘連語〙
❻《「・・・のだった」の形で》㋑ 悔やむ気持ちを表す。・・・しておけばよかった。「こんなことなら予約しておくのだった。」
・・・
（表現）話し言葉では「んだ」となることが多い。
(1) how much of a colloquial expression/slang is it?
It is a colloquial expression, but I don't think it's slang.
(2) what does it come from, grammatically?
is it maybe some kind of abbreviation of んだったらいい？
No, it is not the abbreviation of んだったらいい. I think 「～するんだった」 is similar in meaning and construct to 「～するべきだった」. (べき indicates 当然、義務)
I think that it is pretty often used in casual speech, the way you describe it, to express regret about something you did not do or forgot to do.
「納豆を買うんだった！忘れちゃった。」
The native speaker I am using as my point of reference would more frequently use the above over the one below.
「納豆を買えばよかった。」
I have to admit this is a somewhat unusual way of turning a verb into a past form, but it is very natural expression nonetheless.
Also, from my understanding, the former sentence indicates that you had planned to buy it before you went to the shop, but you forgot, whereas the latter is more like reflecting on your choice after you came back home. "Maybe I should have bought natto?"
すればよかったis more normal.日本人が言うのを聞いても、もしかしたら理解できないときがあるかもしれない