I want to be clear I am not saying the way I split them is correct, its just my guesses at how those more common uses were split or how I was thinking of them. I think 他に could be either depending on the circumstance now that I think of it harder. I was thinking as ほか meaning another, and as a specific thing that is different or other, but you can definitely use 他 adverbially and not simply as I was thinking of it when making those lists. I was referring specifically to ほかに(も)・ほか(に)は (JLPT N4) | Bunpro – Japanese Grammar Explained which I should have said explicitly since in their description they say " Basically, 他 by itself just means ‘another’, or ‘other’. に highlights 他 ‘another thing’ as being the target of what comes next in any particular sentence." And they claim it is the target marking に for this grammar point. But I do think there are other ways to use it that are presumably adverbial.
Much of the way I have learned has come from Cure Dolly’s videos and she seemingly pushes a very different line of logic than a lot of the responses I read on here, she often very much pushes understanding the core parts of a phrase or even idiom to actually get to the core logic of Japanese like with かもしれない and also ように and many others. I suppose it could just be preference of what one finds easier to help them individually, I often find myself very uncomfortable with learning things as set expressions and makes me feel like I am simply memorizing facts about Japanese and not actually learning Japanese. Much like memorizing your times tables is much different than knowing how to do multiplication. They usually go together sure, but if you were to literally just memorize them, you wouldn’t have learned multiplication per se.
I understand this is a very rigid example, and doesn’t completely overlap with the nuance of learning a language, its just the best way I could think of to lay out my point.
I guess I just find it surprising that other’s do not look at it and ask “Which function of the に particle is occurring here” when trying to learn, to me it is just my natural response to want to breakdown and understand a sentence. Maybe I am not looking at it correctly as it seems others do not have this reaction to my examples but tend to lean more towards it being weird that I am thinking of it this way. Maybe adverbially and target based sentences are more similar than I had been thinking of them and it leads to this confusion on my side.
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(〇 幸せを感じる, 〇 幸せな家族)
They take many creative liberties to make them shorter, more snappy etc. I’m not taking the manga titled 「 須波優子と百合な人びと」 as evidence that 百合 is a な-adjective.