Actually I think we have similar thoughts on this. I didn’t bring it up before, but now that you did…
I was reading an article on the necessary vocabulary coverage to be able to understand texts and infer new words from context. Turns out Japanese has an overwhelmingly larger number of words than most/maybe all other languages, and the author was trying to explain the causes behind this.
One of the points the author brought up was that what counts as a word in Japanese is not a straightforward matter, and this could lead to an overestimation. They then showed the following sentence and asked how many words are in there:
食べていらっしゃったらしいから
To me, the answer was obviously 4:
食べて / いらっしゃった / らしい / から
However, a native Japanese commenter said that the example was bad because the answer was obviously 5:
食べ・て・いらっしゃった・らしい・から
The author responded saying the commenter was right, but that foreigners may parse it differently because of how we’re taught it. The fact that there was mutual agreement, and that a Japanese person would call something a simple matter, displaying such great confidence, makes me pretty sure this is not just some dumbass on the internet giving a totally weird idea. It gives me every reason to believe this is how a native Japanese person typically parses the sentence.
Now what this means is that a native Japanese understanding of that sentence separates the て as a whole other, distinct word, while keeping 食べ in its stem!
This got me thinking about the particle で, which is often used to convey the means by which something is done. For instance, バスで行った “went by (means of) bus.” Even when で is use to express reason, as in 病気で倒れた “fell due to illness,” I would insist on understanding it instead as the illness being the means by which the person fell.
With that understanding out of the way, I think the て conjugation in the article’s example sentence is just the same as the で particle. Hence, the sentence should be interpreted something like this:
Because apparently was (gloriously) being by means of eating.
In more natural English, “Because apparently they were eating.” The major difference is 食べ て modifies いらっしゃる, the verb of being, whereas in English, the verb of being modifies the eating.
If we make a simpler version of the sentence:
食べている
I would say to interpret it as 食べ, “eating,” て, “by means of / in the manner of,” and いる, “am/is.” All in all, if speaking about oneself, it would be something like “In the manner of eating is how I am.”
Taking this idea further, I noticed that てくれる and all the giving/receiving grammars that use て really do use this “by means of / in the manner of” understanding of て as its own separate word. For instance, in a song about an ex-girlfriend explaining her reasons to her ex for leaving him for another man, one of the lines is this:
ちゃんと「好きだ」という 言葉でくれるの
Obviously で is a separate word here. But if we had instead done this:
ちゃんと「好きだ」という 言葉を何度も言ってくれるの
we could still separate て out as the manner by which someone says.
So going back to your comment, I think I interpret 参加していない as
参加• し (or 参加し) , then て, so that we have “by manner/means of participating” and then いない, “am not.”
Hope that’s interesting food for thought. Here’s the article I referenced throughout this post: https://linnameigetz.com/japanese-vocabulary#i-5
(sort of why we need full context to vet this grammar scenarios).