Based on the premise, To Shape A Dragon's Breath includes several elements that I love, so I thought that I would like it as well. Especially since a lot of booktokers and bookstagramers that I follow love the book and hype it a lot. Unfortunately, the book fell utterly flat in my opinion.

The biggest issue, for me, is the world-building. The author took our world, and a large chunk of known history, but instead of the British Empire, they let the Norse (Norwegians, Swedes and Danes) become the powerhouse of the world. They conquered Anglesland (England, Scotland and Wales) and became the rulers there instead of vanishing into the Normans and Anglo-Saxons. In addition, the Norse went on conquering Tyskland (Germany), Polland (Poland), Frankland (France), Finnland (Finland) and parts of Russland (Russia). They were at war with Vaskosland (Spain and Portugal) in North America (North Markesland) and came to a peace treaty that gave land below New England to Vaskosland while they kept New England and Canada. Currently, they are fighting against the Natives at the Western Frontier (likely just the area to the West of the Great Lakes). The known world also covers Northern Africa (Furth, Widnes and Coptland are the respective countries that are known in Aprika), Tuscanland (Italy), Turksland (Turkey), Pashanland (likely a reference to Persia), Kindah (Sinai, parts of Palestine and then a large chunk of the Arabic Peninsula), Kedar (Oman and Yemen), Roveland (more or less Central Asia and parts of South-West Asia), Indusland (India), Shiang-Gang (China), Zhongu (Korea), and Zhippon (Japan). In the past, Tyskland used to have quite some influence on the European continent, excelled in natural sciences and was influential in dragon husbandry.
Personally, I would have been ok with such a world if the author had used more time to explain the history. The reader is expected to either know (by unknown devices) about the world to understand it or to go with the flow and ignore their own ignorance because Anequs only learns a tiny part of history. Mostly, the part where it explains why there is so much fucking German Tysklandish in the vocabulary. If you do speak German (either because you are German, Austrian, Swiss German or learned it at one point): it will drive you mad because the book includes sentences like "Marta announced that she'd have Wurzelsalat and Weichkäse, with Pflaumentorte to follow.", which hinders the reading experience a lot. Also, there's zero explanation why Tysklandish is still so prominent in use that children of the upper society have to learn it, why there's a German café in New England, ... - it is only explained why the majority of skiltakraft (the book's version of chemistry) uses Tysklandish to refer to elements, why a hypothesis is called "vermutun" (technically it should be Vermutung but well), ... but not why the photographer is called "lichtbildmacher" or why there's a German café in New England with a German menu. It irked me so much while reading because it isn't logical. In addition to the entire Tysklandish as one of the major languages: the Norse who conquered Anglesland became the Angles/Anglish while they still refer to their Norsklandish heritage. England became England because the Anglo-Saxons bested the Vikings at one point and the leftover Vikings either assimilated into the Anglo-Saxon culture or they left. England refers to the land of the angles. Given the fact that the Norse won against the Anglo-Saxon, there's zero requirement for them to become the Angles nor to develop a culture that refers to the English high society (think the Golden Age under Queen Elizabeth I.) in terms of clothing, behavioural expectations, ... while their political culture is still very Norse with a High King/Queen, jarls, thanes, ... and includes points like holmgangs (duels to the death). It would have been much more interesting to read a novel with a world where the Norse became the major powerhouse and kept their own culture instead of shoehorning parts of it into English history and putting a layer of steampunk on top of it.

My second biggest issue is the writing style, and by extension, the pacing. The writing is very dry and clinical at times. Yes, it plays in a school setting but there's no requirement for the book to read like a fucking textbook. The dialogues are stilted and at times unnecessarily complicated. It doesn't help that the author infodumps the skiltakraft onto the reader while not giving a glossary. Yes, we have a pronunciation guide (please do not get me started on the pronunciation of the German words) but no glossary. I still have no idea what exactly is happening when someone shapes a dragon's breath aside from "it is chemistry and something will be broken into different elements". There's a periodic table at the beginning of the book as it will be mentioned several times during the novel. If you want to understand the elements mentioned there: open an actual periodic table of the elements. The numbers on the table are accurate and line up with the ones of an actual periodic table. E.g., saffle is sulphur. (If you don't look it up, you will struggle with understanding the elements because parts are German, parts are faintly diverted from a Scandinavian language (Sulphur is called "Svavel" in Swedish, which then is changed to "saffle" because I have the feeling that the author might think that's how you say svavel) etc.) If the author doesn't infodump on skiltakraft, the reader has to endure uneventful day-to-day storytelling, which results in the last chapter being a summary of what else is happening. It feels like the publisher told the author to do it, so it wouldn't become a book with 800 pages. If the book is meant to be read as an account of Anequs' becoming a dragoneer/nampeshiweisit, and as a historical record of the growing tension between Angles and natives, it should have been mentioned in a foreword or in the summary. Because as it stands: there's no actual plot until a climax happens extremely late but what is a climax without a plot?

My last issue with the book is Anequs as a character. Oh my God, she is so fucking boring and the quintessential Mary Sue who can never do anything wrong. Of course, she speaks fluently and extremely eloquently despite learning Anglish from novels as she has no formal upbringing. She is utterly perfect and has no flaws. If she is involved in any conflicts it is because she is drawn into them unwillingly and the conflicts arise because of racism. In every conflict, she behaves perfectly and is always extremely morally sound, well-spoken, intelligent, and rational. For fuck's sake, she is supposed to be FIFTEEN YEARS old. Of course, all her arguments are correct but that's not because of how Anequs speaks/argues but because I would have agreed with the idea behind her argument prior. In addition to her perfection: her romances come out of nowhere. There's one scene with Liberty (a young black woman who is basically a slave who can buy herself out of her enslavement) where Liberty takes Anequs measurements for a dress and suddenly Anequs wants to kiss her, which she does in a later scene. There's another scene where Anequs thinks about kissing Theod because they danced a waltz together, and she kisses him in another chapter. There's no chemistry between any pairings. Liberty tells her out of nowhere that they cannot be together because a) homosexuality is bad and b) I have to pay off my enslavement debt. Theod confesses his love for Anequs out of nowhere as well. I don't understand why people are so excited about the poly representation because there isn't really one. Yes, Anequs wants to court both but neither Theod nor Liberty are aware of the situation. Both believe that Anequs will just be courting them in the future.

TL;DR: I am tired and exhausted upon finishing the book. 110% infodumping on fantasy chemistry, no glossary, extremely weird and unsatisfying world-building, and a Mary Sue as main character. If you're an author who plans on creating fantasy chemistry: DO INCLUDE A GLOSSARY! The dragons are boring because you could replace them with a dog and nothing would be changed.