Feeling Nostalgiac for Stationery Shops 文房具屋が懐かしい

I have been fond of stationery shops (since my childhood).

(): Right now, this sounds more formal. To sound more conversational instead you could write, "since I was young". If you want it to be more exaggerated "since I could walk!"
To continue sounding more conversational you could shorten "I have" into I've.

I can spend hours browsing the shelves ofilled with notebooks and pens without buying anything.

When I was a (child), there were several small stationery stores in my neighborhood, but now they have almost disappeared.

Another casual/conversational option could be to use "kid" instead of "child".
For stationery, I would stick to using stationery store like you did here for the rest of the text too. But stationery shop is not wrong.

(These days), I usually buy stationery either at the stationery section of a supermarket, in a shop inside a station building[train] station, or online on Amazon.

(): casual/ conversational option = Nowadays
[]: are you referring to a train station here?

I have been fond of stationery shops since (my) childhood.

or "...since I was a child."

SI feel drawn to the square notebooks and metallic-colored pens attract me, even though they seem impractical.

"Attract" might be too strong a word to use here, so you can simply say "I feel drawn to...".

When I was a child, there were several small stationery stores in my neighborhood, but now they have (all) almost disappeared.

These days, I usually buy stationery either atin the stationeroffice supply section of a supermarket, in a shop inside a station building, or online on Amazon.

The term "station building" isn't common in English. Do you mean train station?
In the US, there's not a specific "stationery section" - all the office supplies are grouped together. Perhaps that what you have as well?

These days, I usually buy stationery either atin the stationery section of a supermarket, in a shop inside a station building, or online on Amazon.

Amazon is so common that we usually don’t bother specifying that it’s online. Perhaps that’s part of the problem!

I miss the old days, when I could wander into a stationery shop with no particular purpose and enjoy discovering new items.

What you wrote is grammatically correct, but when I hear this spoken, there is usually a pause after “old days,” just long enough to give the listener time to conjure up memories!