I really don't think these 'Clara Benson' books were written in the early 20th century. The book is a perfectly fine 'cosy' mystery, but I don't buy the story that it had recently been found by the author's family.
Writers of popular novels from the 1900 - 1930 era, like Jane Abbott, Edgar Wallace, E. Philips Oppenheim, Edna Ferber, Margaret Sydney, Willian McLeod Raine, or Angela Thirkell, include a great deal of description in their novels. Typically, there are pages and pages of detailed description of absolutely everything. Especially if the book is set in a foreign country like this one is. At the time, very few people had the means to do very much traveling, so readers liked finding out about the details of what it's like to live in a place like Italy. There was no television, or magazines, or much of the other media which we take for granted these days. So books were seen as a way to learn about foreign cultures. The food, clothing, family life, architecture, art, even the plants and local animals are all described in novels from this era. . It could be why these writers are not very well known now, it's a different style that seems odd and at times tedious to modern readers. There's none of this type of description in these books. Since there is not as much description as is typical for this era, the plotting is too fast paced to have been from this era.
The vocabulary is also not as complex as the typical novel from this era. Yes, it's sprinkled with a few key phrases, but each sentence is fairly simple and uses common words. Read an old book and the sentences are filled with words that are not very commonly used now, and are much more complex than this.
Also, the attitudes and reactions of the characters are much too modern. It was very rare for a single woman to travel as much as this character does, and she also does it not just as a single woman, but alone as well, with no friend with her. Maybe this is explained in one of the other books, but this really was not common at the time. Isabella Bird was able to do it, but she was the rare exception.
There is a scene where the main character drives a car. Driving was still very uncommon in the 1920's, a bit less in the 30's, but very few people had cars in comparison to the total population, and it was not at all common for women to learn how to drive. Cars of this era are not at all easy to drive, they don't have all the modern conveniences like power steering and automatic transmission, so it's not exactly easy to drive a car from the 1920's, it's a lot of work to just steer the car. In books of this era, there would normally be a detailed description as to how the main character learned how to drive, where they got the car, why they were driving,what an adventure it is to drive. But not here, she just gets in the car and drives.
I would have been much more accepting of the premise if I knew it had been written recently, and it had been released as a mystery that just happens to be set in the 1920's, but being told that it was written close to 100 years ago just ended up getting me irritated. Read a Dorothy Sayers or Agatha Christie instead.