This is a complex issue, and there are a lot of things to consider. Generally, in my experience, it's better to make up a brand of your own, but it depends on what you think would work best for your story, considering the following points:
Not using real brands can give you more creative freedom
Funnily enough, I have an example of this from just the other day. I was writing a scene where my protagonist meets his soon-to-be love interest (who's also secretly a supervillain bank robber) in a nightclub. To demonstrate her wealth, I had her remark, "My entire outfit is Gucci". Then shortly afterwards, I came to a bit where I had to describe her outfit, so I looked up the Gucci women's catalogue.
Let's just say the clothes in their catalogue didn't match the image I had in my head of what that character would actually wear. Especially in a nightclub. Rather than flick through every high-end fashion brand I could think of in search of one that did match, I just changed the line to "My entire outfit is designer" and then made the description up.
Not using real brands lets the reader fill in the gap
Let's say you have a running gag in which your character's smartphone is slow and keeps crashing, and they constantly complain about it. If you don't mention the brand, readers will imagine it to be whichever smartphone company they like the least, and the joke will become even funnier to them. If you mention it's an iPhone, suddenly readers who like iPhones - and Apple's lawyers - aren't laughing anymore.
Using a real brand can help reinforce a character's personality
Certain brands are associated with certain subcultures or personality types. To use the soft drinks example: Mountain Dew is associated with gamers; Faygo is associated with Juggalos; Dr. Pepper is associated with the anime Steins;Gate. You can use these associations to your advantage, either to subtly reinforce a character's personality, or to subvert them ("The hell is a Juggalo? I drink Faygo 'coz it tastes nice.") At the same time, you should avoid a character using a brand that doesn't fit their image (unless, again, it's for subversive purposes).
Using real brands can date your work (but fake brand names are risky too)
This is something you alluded to in the question, but only occurred to me two years down the line:
a small brand [...] might get replaced next year by a better brand, turning my work into a period piece
This can happen with big brands anyway. Look at MySpace and Bebo: around 2007-08, they were two of the biggest social networks, but by about 2012 they'd both faded into irrelevancy as other social networks came along. Now MySpace is only remembered as "that one site nobody goes on anymore", and Bebo isn't remembered at all. Worse, if your story takes place in the future, you run the risk of anachronisms (arguably the most famous being Pan Am's prominent appearance in 2001: A Space Odyssey - they collapsed in 1991).
On the other hand, making up a brand comes with the risk that later on, a real-life brand or organisation will spring up using the same name, and ruin your use of that name in your own story. Consider this question from Feb 2020 in which a user planned to use the name "Corona" in their story, but then COVID-19 came along and made "Corona" synonymous with the worst pandemic in a century.