Had a bit of a google, and apparently it’s only agglutination if it’s a small morpheme, mostly only a single sound, that’s added permanently to a word.
So for example, “an ewt” became “a newt” or “a eke-name” became “a nickname”.
What German does is compound words. Here whole words (not just small morphemes) are added ad-hoc (and not permanently).
You will not find a “Donaudampfschiffkapitänsmütze” in a dictionary. That’s not a “real” word. That’s just jumbling a bunch of words together ad-hoc to be used once and that’s it. Like when you string multiple words together in a sentence.
Sometimes specific words strung together are used so frequently that they become their own word with their own distinct meaning (z.B. Zeitgeist, which consists of Zeit+Geist (Time+Spirit), or Kindergarten, which consists of Kinder+Garten (Children+Garden)).
But initially, it’s just joining words.
This is what Wikipedia has to say about that:
As a member of the Germanic family of languages, English is unusual in that even simple compounds made since the 18th century tend to be written in separate parts. This would be an error in other Germanic languages such as Norwegian, Swedish, Danish, German, and Dutch. However, this is merely an orthographic convention: as in other Germanic languages, arbitrary noun phrases, for example “girl scout troop”, “city council member”, and “cellar door”, can be made up on the spot and used as compound nouns in English too.
For example, German Donaudampfschifffahrtsgesellschaftskapitän would be written in English as “Danube steamship transport company captain” and not as “Danubesteamshiptransportcompanycaptain”.
https://en.m.wikipedia.org/wiki/Compound_(linguistics)
