Dedication (lines 44-48 of the file): to "Frederick Soddy's 'Interpretation Of Radium'", "this story, which owes long passages to the eleventh chapter of that book". The Gutenberg preface says the novel "was written in 1913 and published early in 1914".
In the novel, "Ramsay, Rutherford, and Soddy, in the very beginning of the twentieth century" are named as the starting point; the fictional atomic weapon uses an element "Carolinum".
Google snippets [web, not opened]: Wikipedia (https://en.wikipedia.org/wiki/The_World_Set_Free) and others say the dedicated volume is the 1909 edition; an Amazon snippet says Soddy's Wealth, Virtual Wealth and Debt praises The World Set Free (not checked in the WVWD text in this run).
PMC, Guston 2012 (see that note) says Soddy's reading of the novel reinforced his view that governments would turn any technical resource to war, and that by 1915 he had "recoiled from his glance into the abyss of nuclear warfare" (quoting his nephew via Davies 1992).
How it bears on the claims
Claims 6-7 (release of nuclear energy would bring great energy and great danger; civilisation depends on new energy): Chapter XI of the 1909 edition (see the Internet Archive note: "Transmutation is the key to the internal energy of matter ... Speculations on possible forgotten races of men") is the chapter Wells says he drew on. This is the main documented channel by which Soddy's principle reached a wide public before 1914, and through Wells reached Leo Szilard ([memory], high confidence: Szilard read the novel in 1932; not checked in this run).