1880 Hamburg steak

1902 Hamburger sandwich

"The shortened form burger is attested from 1939; beefburger was attempted 1940, to make the main ingredient more explicit after the -burger had taken on a life of its own as a food suffix (compare cheeseburger, attested by 1938)."
Etymonline

"Burger" seems to be more about being a mince patty, which could be either meat or vegetables.

"Hot dog" could really only be exclusively meat if it were made of actual dogs. Again it seems to be more about presentation than ingredients per se.

I understand the meat industry's concern about making a living, but I find this a bit silly. The fact that much fake meat is not particularly tasty does more for them than having sausage methode chien chaud.

Hamburger - Etymology, Origin & Meaning

Originating in the 1610s from Hamburg, "Hamburger" means a native or ship from Hamburg; later also a Tyrolean grape (1838) and hen variety (1857).

^etymonline

I can find no reference to vegetables in any historical records of the use of Burger, commercially before 1960s.

While recipes for meat-free burgers have been in print since the 60s, the first commercially sold veggie burger came much later in the early '80s and is said to be the brainchild of a natural food restauranteur in London.

The veggie burger was born in 1982: it was an idea of Gregory Sams, the owner of SEED, a vegetarian restaurant in London. The menu Sams offered was inspired by Japanese cuisine and was admired by famous pundits, such as John Lennon and Yoko Ono.

Minced meat was not generally used as a term in burgers or their ingredients.

Burger King (BK) introduced a veggie burger in 2002, the first to be made available nationally in the U.S.

Burger = in the style of Hamburg Germany.
Will the people who are part of the Hamburger Schule of music be required to remove the word "Hamburger" from their movement?
What about Hamburger Rote Grütze? So yummy! No meat in that!

@Andrew Pam