Gu Si Xiang Qu (2023)

Also reverse time travel, so as male lead gets older, he meets a younger version female lead - their timelines/time axis go in opposite directions. Also have years of interval between every meeting. Another tear-jerker!
Need to watch twice to see the other lead's perspective and understand why they say and do some things at the beginning.

Ancient Love Song - travels back in time and interacts with/falls in love with woman who becomes integral to history of the kingdom/becomes Empress. Also affects how things happen.
Splash, Splash, Love - travels back in time and interacts with/falls in love with famous king in Korean history. Also affects how things happen.

Both are short (Splash, Splash Love is shorter), both travel back through a medium - rain puddle/precious stone medallion, both are sweet and poignant.

They both are time travelling themed drama with both sweet and angsty and painful moments. Also in both drama there are palace/political plots.

The story is about two guys meeting and falling in love while living in different timelines. They meet a couple of times at midnight in room 609. There is a lot more to this story than that. But that is what links it to this story.

Time travel and the tragic feeling of being a passerby in someone else's destiny. Shen Buyan is the male version of Ruoxi. Both have epic love stories.

Both show's stories are somehow similar. In Lovesickness, FL time traveled in the ML era, but in An Ancient Love Song, ML time traveled, and they tried to change the history and tragic end of their lover. But in terms of production and story execution, the quality of An Ancient Love Song Show is higher than Lovesickness.

Both these dramas tinker with the concept of time and how that affects the actions of a person, including the biggest question of whether destiny can be changed, though the elements of time travel are more explicit in AALS than SoT. More importantly, they also both have really strong, decisive, and badass FLs who have "soft" and "star-crossed MLs to support them.

Romantic tragedies where the beginning shows you how it’s going to end. You’re rooting for fate to be changed, for these characters to be happy, but you know the pain is coming. Both are well balanced, so it is not all sad all the time.

plot elements and settings are pretty different, but they're both the same type of tragic love story: destined lovers with loves doomed from the very beginning.