The only collective term I can think of, would be 包丁, which means "kitchen knife".
Though, as I've pointed out, that also includes bread knives, paring knives, utility knives, tomato knives, carving knives, boning knives, nakiri, usuba etc

As the page you reference (and any other you can find) makes clear:
A santoku isn't a gyūtō, and a gyūtō is not a santoku.

They are both knives that are intended as a main all-around kitchen knife, but they are not the same knife, nor is one a type of the other.
The same is true of the bunkabōchō (the predecessor of the santoku), though some people (wrongly) regard it as a type of santoku (if anything, it's the other way around), due to their great similarity.

@@ -12 +11,0 @@
-<xref type="see" seq="2070640">三徳包丁</xref>

https://www.jikko.jp/news/difference-between-santoku-gyuto - 三徳包丁と牛刀の違いをご存じでしょうか？この記事では、それぞれの包丁が持つ特徴や、正しい使い方に焦点を当て、あなたにぴったりな一生ものの包丁を見つける手助けをします。家庭用に適した形状で使い勝手抜群の三徳包丁。一方で、牛刀は料理のバリエーションを広げ、食材に合わせた切り方を追求する料理愛好者に向いています。

Maybe an xref to the more collective term.

@@ -11,0 +12 @@
+<xref type="see" seq="2070640">三徳包丁</xref>

Yeah, it's very plausible that 牛刀 may have been used for any knife used for red meat, very early on. It's also plausible, that they mistakenly referred to chef's knives, as butchers' knives ...and continued to keep that mistake in dictionaries, long after the mistake was corrected among chefs, knife makers/sellers, and the general public, due to going with the older dictionaries, that have the "butchers' knife" gloss.

As for "kitchen knife"...
Kitchen knife is a broad category. Kitchen knife doesn't mean chef's knife.
While a chefs' knife is a kitchen knife, so is a bread knife, paring knife, utility knife (not to be confused with non-kitchen utility knives. Called a "petty", by the Japanese), carving knife (this includes sashimi knives, like the yanagiba), boning knife, nakiri, usuba etc. Those are all kitchen knives.

@@ -13 +12,0 @@
-<gloss>kitchen knife</gloss>

Daijs: 牛を切りさくのに用いる大きな包丁。
Daijr: 牛を切り裂く大きな包丁。

I suspect that 牛刀 originally meant "butcher's knife" or "meat ax(e)" and the current meaning has moved on to it being used for the main chef/kitchen knife, which is (also) used for cutting up meat.. I have a 1930s Kenkyusha JE and it just glosses it as "butcher's knife".
I don't call the knife I use for cutting up meat a "butcher's knife", and it's probably inappropriate for 牛刀.

@@ -12,0 +13 @@
+<gloss>kitchen knife</gloss>

https://ja.wikipedia.org/wiki/ナイフ#解体用ナイフ（ブッチャーナイフ）

Note that Japanese Wikipedia's article on ナイフ, lists "解体用ナイフ（ブッチャーナイフ）" as a separate section, to "キッチンナイフ（包丁も含む）".
With 牛刀 mentioned in the "キッチンナイフ（包丁も含む）" section.

When I tried to find "butchers' knife", on Japanese Wikipedia, I searched for ブッチャー, got to https://ja.wikipedia.org/wiki/ブッチャー
Saw "ブッチャー・ナイフ（Butcher knife） - 肉を切るナイフ", clicked on the link to "ブッチャー・ナイフ" ...and got to the referenced section.

https://en.wikipedia.org/wiki/Butcher_knife
https://ja.wikipedia.org/wiki/牛刀
https://foodsguy.com/cleaver-vs-butcher-knife/
https://barbecuefaq.com/butcher-knife-vs-chef-knife/
https://cdn.shopify.com/s/files/1/2149/7399/articles/Featurephoto_7c12f87a-298f-4794-99c6-475b34fed9ec.jpg?v=1609130712
https://dalstrong.com/blogs/news/cleaver-knife-vs-butcher-knife-what-s-the-difference

Here are some refs. (didn't see them as necessary, but if they are, these are some quick examples)

Also:
Just looking at the pictures, from an image search, and actually looking up info, are two very different things.
An image search can give you a quick impression of what a word typically refers to ...but that impression won't necessarily be _reliable or trustworthy._
Also, if you do an image search for "butchers' knife", you get nothing that looks like a chef's knife. You also get a lot of cleavers, though (despite what many believe) those aren't actually butchers' knives.

Aside from the fact that butcher's knives look notably different:
Knives can look the same, in profile, but be completely different and have completely different things they can or can't do, and for which they are or aren't suited.
For example: A Chinese chef's knife looks like a cleaver, but can't cut through bone. A nakiri or usuba (knives for cutting vegetable) look much the same as a nata. (bushcraft/woodcraft knife. Can even be used to chop wood, by batoning. Well, small nata can't manage that, but any that are at least as big as a nakiri or usuba...)

@@ -13 +12,0 @@
-<gloss>butcher's knife</gloss>

GG5: a butcher knife; a cleaver; a meat-ax.
中辞典: a butcher knife
プログレッシブ: a cleaver; a meat-ax; a butcher knife
Reverso: several matches with butcher's knife

You really need to provide references when proposing such an edit. Assertions are not enough.
That said, WWW images for 牛刀 show the sorts of knives I associate with Japanese kitchens and chefs. I'm not really familiar with what butchers use, but they may well be similar.

@@ -12,0 +13 @@
+<gloss>butcher's knife</gloss>

牛刀 is the Japanese word for chef's knife.
Where the idea of it meaning cleaver or butchers' knife comes from, I don't know, but... It is just used to refer to chef's knife.
I.e. the regular standard Western kitchen knife (outside Japan, it refers to Japanese versions of it) ...which obviously isn't a cleaver or butchers' knife.

@@ -12 +11,0 @@
-<gloss>butcher's knife</gloss>

http://ja.wikipedia.org/wiki/牛刀
GG5, 新和英中辞典, Daijr, etc.
cf. http://en.wikipedia.org/wiki/Cleaver_(knife)

From the many images of 牛刀, I'd say "cleaver" is a poor translation. Wikip says: "A cleaver is a large knife that varies in its shape but usually resembles a rectangular-bladed hatchet.", That's not a 牛刀.

@@ -12,2 +12,1 @@
-<s_inf>Often translated as cleaver, but used for slicing meat, not cleaving bone.</s_inf>
-<gloss>meat cleaver</gloss>
+<gloss>butcher's knife</gloss>

http://ja.wikipedia.org/wiki/牛刀

Note on “cleaver” – this is a common loose translation of Japanese and Chinese chef’s knives, though they are not actually used as cleavers.

@@ -12,0 +12,1 @@
+<s_inf>Often translated as cleaver, but used for slicing meat, not cleaving bone.</s_inf>
@@ -13,0 +14,1 @@
+<gloss>chef's knife</gloss>