The Silver Case is a game whose strengths are based on "vibes" rather than plot or intrigue.
There is a story that's happening here - you investigate a series of murders happening in the fictional Ward 24 of Tokyo. Yet none of it feels important and I think that's intentional. When dramatic events occur it never feels shocking. Instead, it's all part of a relaxed and meandering mood where you just let it wash over you. I don't know if this is a good comparison, but it's similar to how I felt with Serial Experiments Lain. You don't need to follow the specific events of the story or even the lengthy infodumps that both The Silver Case and Lain drop on you to enjoy what's on offer.
The writing is clunky in a way that evokes the charm of late-90s localised games. Thankfully it's not difficult to parse, instead helping drive the atmosphere of a city where everyone and everything is odd in some way.
There are some puzzles that I found to be unengaging, but the game offers you the choice to skip them and it isn't long until they just stop appearing altogether, the game instead focusing entirely on its tone and narrative.
The Silver Case is tricky to recommend but for those who it will click with, it'll click hard.