3 adjectives (in different classes) describing a noun & commas

In the case of three adjectives, can there be a combination of classes and therefore commas? A bit confused.

Eg.

In the early 1900s, many poor, uneducated German immigrants settled in the town.

"poor" and "uneducated" seem to be interchangeable and need commas, but then "German" seems to be another class.

If there were only two adjectives ("uneducated" and "German"), I would not put a comma. But if it were only "poor" and "educated" I would. I think that would be correct. But in the case above, with 3 adjectives, should there be a comma after "uneducated"? In general with 3 adjectives, should there be commas after the first two or does it depend also on classes?

I'm open to people telling me that I'm wrong, but it seems to me that the reason there is no comma between "German" and "immigrants" is due the the specificity of the immigrants being German. Because of this, "German immigrants" acts as one noun. I think of it as being similar to a sentence such as:

Her lyrical, elegant public speaking helped her to win the election.

Even though, with analysis, one could conclude that the word, public, is a modifier of the "bare noun", speaking, I feel quite confident saying that "public speaking" stands as a noun on its own.

I found something a bit more technical that I think can help answer your question.

PRONUNCIATION

Stress is important in pronunciation, as it distinguishes between a compound noun and an adjective with a noun. In compound nouns, the stress usually falls on the first syllable.

While I usually thought of a compound noun as being one word with the parts squished together, Wikipedia gives examples of compound nouns with spaces in between the constituents. I think that the whole article on compound nouns could be useful were a discussion to ensue from this post. The bold-faced emphasis is mine.

Types of compound nouns

Since English is a mostly analytic language, unlike most other Germanic languages, it creates compounds by concatenating words without case markers. As in other Germanic languages, the compounds may be arbitrarily long. However, this is obscured by the fact that the written representation of long compounds always contains spaces. Short compounds may be written in three different ways, which do not correspond to different pronunciations, however:

• The "solid" or "closed" forms in which two usually moderately short words appear together as one. Solid compounds most likely consist of short (monosyllabic) units that often have been established in the language for a long time. Examples are housewife, lawsuit, wallpaper, basketball.

• The hyphenated form in which two or more words are connected by a hyphen. Compounds that contain affixes, such as house-build(er) and single-mind(ed)(ness), as well as adjective–adjective compounds and verb–verb compounds, such as blue-green and freeze-dried, are often hyphenated. Compounds that contain articles, prepositions or conjunctions, such as rent-a-cop, mother-of-pearl and salt-and-pepper, are also often hyphenated.

• The open or spaced form consisting of newer combinations of usually longer words, such as distance learning, player piano, lawn tennis.

Usage in the US and in the UK differs and often depends on the individual choice of the writer rather than on a hard-and-fast rule; therefore, open, hyphenated, and closed forms may be encountered for the same compound noun, such as the triplets container ship/container-ship/containership and particle board/particle-board/particleboard.

In addition to this native English compounding, there is the classical type, which consists of words derived from Latin, as horticulture, and those of Greek origin, such as photography, the components of which are in bound form (connected by connecting vowels, which are most often -i- and -o- in Latin and Greek respectively) and cannot stand alone.