The Wiki article intermixes Umlaut in the sense of a special vowel/letter with Umlaut as the historic process of vowel alteration in the Germanic languages (= Umlauten; Umlautung). "assimilierend" and "angeglichen" is a tautology (aimed at jargon-dropping). My attempt at an explanatory translation of the clumsy Wiki-German:

The process of Germanic Umlautung consisted in assimilating the pronunciation of a vowel to that of a vowel or semivowel in the syllable before or after it, which resulted, for instance, in the alteration of a vowel before an /i/-sound to /i/.

Proto-Germanic setjan (e + j) thus came to be altered to sitzen or sit.

So leicht geht das. :-)

Tipp: Schau mal im Duden nach "Umlaut":

1. Veränderung eines Vokals, besonders der Wechsel eines a, o, u, au zu ä, ö, ü, äu

2. a) durch Umlauten entstehender Vokal bzw. Diphthong

2. b) Buchstabe, der für einen Umlaut (2a) stehen kann (ä, ö, ü)

Anscheinend beizieht sich der Wiki-Artikel nicht auf die Bedeutung 2, also den tatsächlich gesprochenen Vokal oder Doppelvokal (Diphtong) (2a) oder die/die dafür geschriebenen Buchstaben(2b), sondern auf die Bedeutung 1, den Wandel des Vokals (z.B. bei Pluralbildung "Hahn" -> Hähne")

Siehe auch:

Merriam-Webster assimilation 

3 phonetics : change of a sound in speech so that it becomes identical with or similar to a neighboring sound

und en-Wikipedia Assimilation (phonology)

Assimilation is a sound change in which some phonemes (typically consonants or vowels) change to become more similar to other nearby sounds.

Ganz ehrlich gesagt, jene Bedeutung 1. des Duden war mir bisher völlig unbekannt, und mir will das auf die Schnelle auch nicht alles richtig einleuchten. Aber die Übersetzung scheint zu stimmen.:-)

Let me start with the meaning. Umlaut is a process where the pronunciation of a vowel changes (from its original sound) as a result of the influence of the pronunciation of the following vowel or diphthong.

Note, the German says "umgebende Silbe", but the examples in the article are only of a "folgende Silbe", so I took the liberty of saying "following vowel" in my explanation.

This kind of change is one example of what linguists call "assimilation". See https://psychology.fandom.com/wiki/Assimilati... for further explanation and examples in English.

If you follow the link in your citation to "i-Umlaut" you'll see the example of the change from *kuningaz to künic to modern König; the /u/ sound was assimilated to the following /i/, the tongue brought through time more to the front of the mouth, first to /ü/, and currently to /ö/.

I hope that helps somewhat...

@Rominara – Thank you for the explanation and the translation.

I'm particularly trying to figure out the syntax, especially how does assimilierend work.

Also, is angeblichen a typo for angeglichen?

Can you (or anyone) offer an exact translation?

Assimilierend (as I see it) functions as an adverb, "through assimilation", or "in an assimilating fashion", or something similar.

I don't see any angeblichen; the original has angeglichen.

I can offer a translation; but I'm a little intimidated by your request for an exact translation. I'll wait for the pros.

@#4: Also, is angeblichen a typo for angeglichen?

Das ist eher ein Lesefehler? Die Variante mit "b" habe ich nirgends gesehen.

____

@#1:

"The Wiki article intermixes Umlaut..."

Das tun anscheinend schon die Quellen. Mir wäre es auch eingängiger, wenn Duden und MW den Vorgang nicht "Umlaut", sondern "Umlautung" nennen würden. Tun sie aber nun mal nicht.

(Vielleicht verstehe ich das auch noch nicht ganz richtig, die Sache ist für mich neu)

#6: should read: for example as an /i/ alteration before an /i/ sound.

Re #6 and #8. Rather than "/i/ alteration" or "altered /i/ ", I would suggest either leaving "i-Umlaut" untranslated, or else translating it as "i-mutation" or "front mutation" or even "fronted vowel "; see e.g. https://en.wikipedia.org/wiki/I-mutation

Siehe auch Assimilation (Phonologie) in Wikipedia. Dort verlinkt Assimilation (phonology)  

edit: hat Harald in #2 auch schon geschrieben.

I'm particularly trying to figure out the syntax, especially how does assimilierend work.

I agree with Rominara that "assimilierend" is tautological in this sentence and just bad style.

"wurde assimilierend angeglichen" is like "was assimilatingly adapted" i.e. adapted by assimilating it.

If you reduce the sentence to its core message, you get:

Dabei wurde XX assimilierend (= durch Assimilation) dem YY angeglichen.

Does that help?