easiest way to aggregate values over multiple columns?

I have a table that looks like this:

My goal is to make a summary of each animal based on their classification, i.e. basically just to get a count of each animal and their corresponding classification such that:

The way I did this (and this might be a very beginner solution, I'm afraid I'm making it more complicated than it should be) is by doing the following:

First, I work in the second column. I get the unique list of all animals using array formula, unique, and flatten at the same time like:

=ARRAYFORMULA(UNIQUE(FLATTEN(B2:D)))

This gives me a list of all the animals from columns B to D.

Then, to get the value in the first column, I add a column in the original raw file that concatenates the animals in the 3 columns:

Then I use index match to get the classification

From there, I just use a COUNTIF on the third column to count the instances of each animal in the columns B:D

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You may try:

=index(let(Σ,tocol(if(len(B2:D),A2:A&"|"&B2:D,),1),
           sort({split(unique(Σ),"|"),countif(Σ,unique(Σ))})))

There's nothing wrong with how you solved the problem. I personally try to avoid helper columns, especially for simple problems so here's how I would do it.

=SORT(LET(cc,TOCOL(A2:A&"ζ"&B2:D),QUERY(UNIQUE({SPLIT(cc,"ζ"),COUNTIF(cc,cc)}),"WHERE Col2 IS NOT NULL")),1,0)

First we unpivot the table, then we run a COUNTIF and finally we remove the duplicate and blank rows and sort the result.

Btw, UNIQUE(FLATTEN(B2:D)) is not an array formula so you don't need an ARRAYFORMULA wrapper around it. Also, we have TOCOL now, which is a better version of FLATTEN, I recommend checking it out.