昭和の香り (Shōwa no kaori) and 昭和の匂い (“Shōwa no nioi”) literally mean “smell of 昭和 (Shōwa)”. 昭和 is the Japanese imperial era that lasted from 1926 to 1989, and “smell of Shōwa” figuratively describes something that is old-fashioned or brings back a sense of nostalgia. It can be either positive (“retro/nostalgic/traditional”) or negative (“old-fashioned”) depending on the context. On the other hand, the word ‘昭和臭い’ (Shōwa kusai), which means “stink like Shōwa”, usually contains a negative sense.
Meaning of 昭和 (Shōwa) as a Word
Since the Shōwa era generations are over 30 (in 2020), the term “Shōwa” itself came to have the meaning of “old”, “old-fashioned”, or “traditional”. For instance, 昭和な雰囲気(ふんいき) means “Shōwa-ish (traditional/nostalgic) atmosphere” and 昭和な企業(きぎょう) (Shōwa na kigyou) means “Shōwa-ish company (e.g. a company that implements old fashioned rules/regulations)”.
Learn more details about the era (e.g. its origin and zeitgeist) in the previous post:
Origin and Meaning of the Japanese Era “Shōwa (昭和)”
By the way, the current era is called 令和 (Reiwa), which started in 2019. You can check its origin and meaning in the following post:
Origin and Meaning of Reiwa (令和), Japan’s New Imperial Era
That suit kind of “stinks like Shōwa”
= That suit is kind of old-fashioned and uncool (and reminds me of the Shōwa era).
I went to the cafe that scented “the smell of Shōwa”.
= I went to the cafe that has a nostalgic atmosphere.
The idea that women should not work and stay at home is quite Shōwa-ish (old-fashioned).
レトロな “retro”, “nostalgic”