It is easy to find search results answering this, from sites for private/commercial vet businesses. I was hoping someone might know of something answering this that is more independently authoritative, like a medical vet board for example.
The German Society for Medical Science of Animal's Teeth ("Deutsche Gesellschaft für Tierzahnheilkunde"), a subset of the German Society for Animal's Health, provides a set of codes of practice for all German vets about how to act.
One of them is about the dental care of pets, in context of dog parlor businesses. Some dog parlors in Germany were offering dental care with the promise "that there is no anesthesia needed" because they use ultrasonic sound to clean. This society debates the quality such businesses could provide without hurting the animal, against the cruelty to make a real professional dental cleaning without narcosis. They conclude that it is not possible to clean the important areas of teeth (especially the border between root and skin) without cruel pain for the animal if a narcosis is not administered. Also, it is not possible to polish the teeth after the ultrasonic sound treatment, which is mandatory to smooth the scratches caused by the ultrasonic sound treatment. Without this, the bacteria/plaque would come back faster and easier than before.
In this code of practice is also written:
Daher sollte neben häuslicher Zahnpflege jährlich mindestens eine Kontrolle der Maulgesundheit von Hund und Katze in der Tierarztpraxis erfolgen, um eine not-wendige Behandlungsbedürftigkeit rechtzeitig zu erkennen.
Therefore, in addition to home dental care, the oral health of dogs and cats should be checked annually in the veterinary practice in order to diagnose the need of treatment at the right time.
The Clinic for Small Domesticated Animals ("Klinik für kleine Haustiere" ★ ) of the University of Berlin also states, that the dental health of pets should be researched regularly on vet's visits, to notice changes which need an intervention. They also write:
Sinn der "dental homecare" ist es, im Anschluss an eine professionelle Zahnreinigung unter Narkose eine erneute Ansammlung von Zahnbelägen (Plaque, Zahnstein) zu verhindern oder zumindest zu minimieren. Zähneputzen stellt dabei die effektivste Methode dar, wobei dieses idealerweise täglich erfolgen sollte. Alternativ oder in Kombination zum Zähneputzen können Hund und Katze spezielle Zahndiäten mit mechanischem Zahnreinigungseffekt oder spezielle Zahnpflegeprodukte in Form von Kaustreifen, -knochen etc. angeboten werden.
The purpose of the dental home-care is to prevent or at least minimize new accumulation of plaque or dental calculus after the professional dental cleaning under narcosis. Brushing the teeth is the most effective method there, and ideally should be done daily. As an alternative or in combination with brushing the teeth, dogs and cats could be offered special diets with a mechanical tooth-cleaning effect or special dental care products in the form of Kaustreifen ★★, Kauknochen ★★, and similar.
( ★ in Germany, all domesticated animals are called "Haustiere", there is no difference between a cow, a turtle, or a rabbit, so "kleine Haustiere" (small domesticated animals) are pets, while "Großtiere" would include horse, cow and pig.)
( ★★ "Kaustreifen": strips of dried meat or something similar which the dog needs to chew for a long time before it could be swallowed. "Kauknochen" most times are made from such dried meat/skin, and shaped like a bone. Some are filled with tasty stuff, others are woven out of multiple strips, so it is more difficult to tearing parts of. One famous thing in this category are dried ears of pigs in Germany.)
Pet owner needs to choose the real professional dental cleaning for their pets, and needs to be aware that the critical areas could not be cleaned without narcosis. So other dental cleaning is cosmetic only, not preventing the real health risks. And the owner itself can provide dental home-care and so increase the time between two needed professional dental cares for the pet.