Is "flowery language" frowned upon in engineering and STEM related research?

There's nothing wrong with long words. The real issue with your writing is that it is redundant.

"these related works are germane to our present discussion."

In this sentence, "germane" just stands for "related", so you're effectively saying "these related works are related". Here you are using the English cliche of pairing a common word with a rare synonym, which we also see in phrases like "trials and tribulations" or "vim and vigor". As in these examples, you include the common word because without it, people won't always know what the rare word means. But the very act of doing that makes the rare word completely useless. Redundancy in this form should basically always be removed.

"...therefore, the scenario considered in [reference] is situated diametrically opposite to ours."

This is another example of the cliche above. The word "diametrically" isn't doing any work the word "opposite" isn't already doing. It's only there for the purpose of being a long word.

"The experiments in [references] corroborates with our results".

This is not correct usage: the word "with" shouldn't be there. Incorrect usage of a long word is very bad: people who don't know it will be annoyed with you, and people who do will judge you.

The rule is:

Never use an uncommon word where a common word can do the job just as well.

This is to make it easier to read your work.

You said

My intention is merely for the writing to be conversational

However, "Germane," "Scenario," and "Diametrically" are not words used in conversation. Words like these will immediately jump out to native English speakers as inappropriate for scientific language. In my personal experience, highly educated native Chinese speakers know these uncommon words and use them in their writing, but some native English speakers will not know them and quite a lot of other English language learners, who are the majority of your readership, will not know them.

Write as simply as possible, but no simpler.

Yeah, I've had this before. My PhD supervisor* removed several of my perfectly fine English words with simpler ones. I still have the svn commit message saying, basically: "removing difficult words, but I'll allow 'aberrant'. I've learned something today :)".

In hindsight, I am not convinced that my supervisor was wrong. While my words were accurate, it doesn't hurt to write papers in a form that is more easily accessible to a wide audience. After all, I would like my papers to be read by an audience that does not exclusively stem from a native English speaking country. There are 1.1 billion Chinese people on this planet, and they encompass a substantial number of scientists.

The "corroborates->collaborates" suggestion is obviously wrong, and you can respectfully point that out to your co-author. But for the other two suggestions, I tend to agree with your co-authors that going for a simpler, shorter version is probably a better idea. For instance, where you write "these related works are germane to our present discussion", what is the point of the sentence anyway? Obviously, any related work that you discuss is assumed to be relevant to the discussion in the paper that you currently write, because everyone assumes that you're not wasting everyone's time. And where you write: "...therefore, the scenario considered in [reference] is situated diametrically opposite to ours.", you can also write "hence, the scenario from [x] is the polar opposite of ours". I don't think that the one version is necessarily better than the other, but I do think that they hold the same information, and if one version makes your co-authors happier than the other, then why not go for that version?

*my PhD and subsequent research is in the field of data mining, so definitely STEM.