The APA 7th edition manual states that a citation for an authored e-book without a DOI, if it has a nondatabase URL, should conclude with that URL.
If the e-book is from an academic research database and does not have a DOI, but there is a stable URL (sometimes called a permalink), then your citation should include the URL of the book in the reference. Do not include the name of the database in the citation.
For example, the citation for the e-book The Science of Human Perfection: How Genes Became the Heart of American Medicine, which can be found in the database JSTOR, would look like this:
Comfort, N. (2012). The Science of Human Perfection: How Genes Became the Heart of American Medicine. Yale University Press. http://www.jstor.org/stable/j.ctt32bqd2
If the e-book is from an academic research database and there is neither a DOI nor a stable URL, then just end the e-book reference after the publisher name. You should not include the name of the database in the citation. In this case, the citation looks like a reference for a print book.