I wonder sometimes if I am guilty of sending too much feedback on lessons and reviews. I often find things that I think are a little (or a lot) wrong, and I often don’t get satisfactory responses to my feedback (not complaining here, as I said I probably send too much). I realize that if I was in a college class and had an issue with my textbook, I might start a discussion with my professor (or my peers), rather than simply emailing the authors of the book. In that spirit, and since I have no professor here… hello peers!
I will also own my ignorance here; I have not even completed all the N4 grammar points yet (and in fewer than 24 hours, I will be failing the N4 JLPT 
). A lot of the conclusions I’m about to present were arrived at with the help of ChatGPT. I know how big a can of worms that is around here, but I’ve found that rather than simply asking one question and blindly believing the output, I can ask many questions and compare the outputs (a) to each other and (b) to things which I do already solidly know. And as a sidenote, I have not found it to be wrong yet (which isn’t surprising, since parsing human language is its greatest strength).
The lesson ても (JLPT N4) | Bunpro says that for na-adjectives and nouns, we do:
［な］Adjective＋で＋も
Noun＋で＋も
And for negatives:
［な］Adjective＋でなくて(1)＋も
Noun＋でなくて(1)＋も
I often get confused about the difference between でない and ではない, so I decided to dig deeper here. The end of the lesson contains this “fun fact”:
でも (the form after nouns and な-Adjectives) is often considered to be an adverbial particle itself, and there is often debate amongst native speakers as to whether でも is actually a word, or simply a standard grouping of で, the case-marking particle and も, the adverbial particle. However, It may be easier to remember でも as its own word, for learning purposes.
To present my point immediately (with the bolded emphasis above added by me): I believe this is not correct at all, and that in the case of a na-adjective, で will never be a case-marking particle (rather it is a copula). In the case of a noun, it can be either a case-marking particle or a copula, but the latter is significantly more common. Meaning, this “fun fact” is very misleading (since it presents a corner case as the only case). I spent an hour last night in deep confusion over this, convinced that ChatGPT had to be wrong, and trying to prove it through many queries. I’m not angry though, it was a fun exercise both in learning to (cautiously) use ChatGPT as a powerful tool, and also in solidifying my own deeper understanding of one tiny grammar point.
Another large issue with the lesson (and another reason I got so confused) is that none of the examples actually use で, so I tried to construct my own, keeping in mind this bit from the lesson:
This grammar pattern may also be used for highlighting negative sentences, and will translate similarly to ‘even if not (A)’, or ‘even though not (A)’ in these cases.
I chose an na-adjective randomly, きれい, and formed the construct きれいでなくても, which I figured should mean “even if not pretty”. ChatGPT kept telling me that で here was the て form of the copula だ (which I did not even know had a て form 
), and I kept trying to prove it wrong. Eventually, I was able to parse my own painfully literal meaning of this phrase: “pretty, it is and, not and, even if”. Or more naturally: “even if it is not pretty”. Which is in line with the “even if not (A)” from above.
More thoughts:
The case-marking particle particle で, per で (JLPT N5) | Bunpro is:
always used to highlight something that is ‘required’ to perform some sort of action.
AFAICT, this “something” must be a noun (please correct me if this is wrong). It can never be a na-adjective. And if it is a noun, in a Noun＋で＋**も** construct, sentences where it is a copula are (according to my trusted robot friend and also my gut instinct) much more common than sentences where it is a case-marking particle (since “existence” is a more fundamental concept than “case”, and probably discussed far more often).
If you’ve read this far, thanks for joining me in my dark rabbit hole. I welcome any and all thoughts/criticisms/corrections. 
Oh… and to circle back to the “fun fact” that got my started down this tunnel: I think I can now contribute to the “debate” it alludes to. If the で in でも is not even always the same thing (i.e. sometimes a copula and sometimes a particle), I think that fuels the side of the argument that claims that でも is a combination of two other constructs (either two particles or more commonly copula + particle), and cannot be safely considered its own standalone particle. Though I will admit this is still open for debate.