All the information I try to find on dearu grammar rules, I only manage to
find forum answers that it's a formal, written replacement of desu/da.

However sentences like "私の責任｛せきにん｝であることは承知｛しょうち｝します。" where it's used in the
middle of sentences clearly don't allow for a desu/da to be inserted
haphazardly. I could see that people would want to use dearu beyond formality
so as to use the sentence structure to fit in more details into one sentence
instead of ending it with "私の責任です。承知します。"?

What are the grammar rules for dearu besides the obvious replacement for
desu/da that clearly does not encompass nearly everything function of dearu
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grammar
Language rules of である beyond simply replacing です、だ
This question seems rather open-ended to me.

Subordinate clauses you mentioned. Another common use of de aru is in negating
adjectives:

元気でない

> However sentences like "watashi no sekinin de aru koto ha shouchishiteimasu"
> where it's used in the middle of words clearly don't allow for a desu/da to
> be inserted haphazardly.

I'm not so sure about that, you can easily modify that to "Watashi no sekinin
da to iu koto wa shouchi shite imasu".
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Your understanding of `dearu` is correct. I think the point that makes it
confusing for you here is `koto`. The word represents something like `the fact
that` or `the matter that` in English, and you can have a complete single
sentence before it.

There are some varieties in the use of `koto`, so how about digging into it
and learn this useful word? I think [this
column](https://kawakawalearningstudio.com/all/koto-mean-using-koto/) is
explaining it well.
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> …on dearu grammar rules, I only manage to find forum answers that it's a
> formal, written replacement of desu/da.

Indeed, as you mentioned, である can replace だ/です for formality; notably in
literature. This much is true.

> …where it's used, in the middle of [a sentence], clearly [doesn't] allow for
> …desu/da to be inserted haphazardly.

Correct, that's an important observation. In the famous book _A Dictionary of
Intermediate Japanese Grammar_ , they explain that である can also be used as a
"prenominal form" in the middle of sentences, whilst だ and です cannot.

This raises the question: _" What is a prenominal form?"_

It means である must precede a noun and somehow connect a description to it. It's
like the formal version of the 「の」 particle, which incidentally is
interchangeable with である in many such cases.

In your example, である has effectively replaced the 「の」 particle to make the
sentence more formal.

I've included a reference with the page number for your further reading. I
know you asked this question a year ago, but the answer I found is quite
different to the answers that already exist here, so I hope this helps!

* * *

**Reference:** Makino, Seiichi; Tsutsui, Michio (1995). A Dictionary of
Intermediate Japanese Grammar (50 ed.). Tokyo, Japan: The Japan Times. p. 33.
ISBN 978-47-89007-75-7.
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I think it must be pointed out, that lack of spaces in the Japanese language
is causing some confusion here.

The use of である that you quote here

私の責任であることは承知します。

is not one suffix word である as in 吾輩は猫である。

わたし の せきにん で ある こと は しょうち します

Break it down and you see what's happening here. The "で" here is the same as
the "で" in:

今日 で 春休み は おわり です。

So, don't smush the で and ある together and try to make sense of it as である.
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