Similar to passé is the term dated (Collins) which may seem less freighted.

adding: The difference (to my ear) between passé and dated is that the former has an implication of fashion, faddism or popularity (which the OP did refer to), while the latter is more neutral, meaning only "from an earlier time".

“Old-fashioned” is the old-fashioned way of saying “old-school”.

e.g. They have a very old-fashioned management structure.

This is generally negative in implication, as in the above, although not always:

e.g. I’m an old-fashioned girl.

“Out of fashion” is a more neutral phrase that is actually used in the question to define a slang alternative.

e.g. Fur coats have gone out of fashion. (From the Cambridge Dictionary)

I actually think it is more neutral than passé, which is just the French for old-fashioned, would only work with an audience of a certain education, and may soon become passé.

“Unfashionable” is a single word that is a also more neutral than old-fashioned. This can be seen in the following example:

Although extremely unfashionable at the moment, group selection is an attractive theory when one is presented by data such as this book contains.

The writer is making a positive statement about something that is unfashionable.

I think vintage is pretty neutral and close to what you're looking for.

From Merriam-Webster:

adjective

...

3 a : dating from the past : OLD

   b : OUTMODED, OLD-FASHIONED

Old-school tends to have positive connotations (like, 'Oh cool, that's so old-school!'), passé tends to have negative connotations (like, 'Ugh, that's so passé.'), retro is the most neutral (which fits your example, like old-school--probably the only ones that would really be used in that scenario). Though this means that it is used again (maybe popular or not so much), but with a trending video in your example, that's the case you are looking for. Though in most cases of things being in style, the question is often if something is in style now. So one can have something from recent times that can be old-school, passé, or retro. But if you are referring to something that exists only in the past, old-school or passé would apply, but not retro. Dated is often used to say someone's views are no longer well accepted (and are unlikely to be popular again, if they ever were that popular), but can apply to other things, like methods no longer used. Vintage generally just means something that is old, but doesn't always mean it was popular before.

retro
/ˈretrō/

adjective

imitative of a style, fashion, or design from the recent past.
"retro 60s fashions"

noun

clothes or music whose style or design is imitative of those of the recent past.
"a look that mixes Italian casual wear and American retro"

Démodé could also be used in this context -

Démodé

/deɪˈməʊdeɪ/

adjective

: no longer fashionable

Example sentence -

An old-line French restaurant with stodgy food and a démodé décor
straight out of the 1950s.

(Meriam Webster)

If yesterday is too informal, then you won’t like this too much. However, specifically for pop-culture references like your music video example, you can describe it by the decade it represents:

that hair is so 70s

those shoulder pads are so 80s

These very clearly connote past and passed popularity, while also providing a bit more specificity.