On e of the funniest uses of birthday seaweed soup occurs during the wonderful romcom A DIVORCE ATTORNEY IN LOVE starring Jo Yeo-jeong. Not once but twice in that show our ML played by Yeon Woojin has his birthday seaweed soup dumped on his head (and before that Jo Yeo-jeong discovers the hard way that she bought enough dried seaweed for 100 servings- oops). This slapstick type comedy is all the more effective for being reprised.

I just now realized that I think serving seaweed soup on a birthday is common knowledge.
Like- should everyone know this?
However, I didn’t know about this tradition prior to Kdramas.

For me seaweed soup will always make me think of Reply 1988. For Dong-ryong, the soup isn’t just food or birthday tradition, it’s a rare sign of his mother’s attention. As a working mother myself, it brings back my own regret of how much I or my kids have missed because of the times we were living and the social construct we had to adapt to.

The first drama which comes to my mind is Because this is our first life.
I think it was the show which made me learn about that tradition.

Eun-tak makes seaweed soup on her 19th birthday in Goblin. Of course the more memorable scene is later when she gets a birthday cake for herself and blows out the candles while wishing for a job, getting rid of the aunt and her family and getting a boyfriend. 😂

In Legend of the Blue Sea, Si-A brings seaweed soup to Joon-Jae's house on his birthday. It was made by JJ's mom who's been missing for years and who's working incognito as a house helper at SA's house, and he remembers the taste and the inclusion of sea urchins reminds him of his mom but of course doesn't know she made it.

Hmm I vaguely recall a seaweed soup scene in Nevertheless, can't say between who though. I'm blank. I just know there is one hah.
There's also another drama that I saw really long ago, where the FL soaks a whole packet of seaweed and ends with wayyyy too much. Again, can't remember the name. Damn my aging brain.
Most recently though, 2 days ago, I was watching a food show called No Taste Like Home (Nat Geo). In one ep, the actor Awkwafina visits Korea for the first time, and has seaweed soup made for her. It was an emotional scene, because she had last eaten it at age 4, before her Korean mother passed away, so it was truly a homecoming to her motherland for her.
It was also the first time I heard the story behind seaweed soup, and it's a beautiful one.

Oh so many! First to come to mind was Hometown Cha Cha Cha. She can't cook but she has a sink full of seaweed. it's too salty to eat.

The second was Mr. Plankton. I have kind of vague memories of this, but I think he puts the ring in the soup and she chips her tooth. Also they don't know her actual birthday because she was a foster child so he has a cupboard full of seaweed soup mix. Is that right?

I know there are plenty of others. They'll come to me in the middle of the night!

Healer! Jung-hoo's Teacher tries to make him seaweed soup but fails utterly because he has no idea how to cook. It's an important relationship moment, since Teacher is Jung-hoo's only parental figure.

Kang Soon-Duk (Kim Mi-Kyung) preparing seaweed soup for Ko Moon-Young (Seo Ye-Ji) in It's Okay Not To Be Okay. Moon-Young being her usual brash self when she was being served the seaweed soup, but when she was left alone she was eating spoonfuls of rice with her soup.

I have a vague recollection of Hometown Cha Cha Cha, I think, where Shin Mina's character makes 미역국 for Dusik, and he can't fathom how she made it taste so bad.

Did I dream this or am I getting confused with another drama?

Very.
Interesting to read below about the origins of this tradition.

My most recent drama watch my daughter's so young.Featured this soup a few different times.