I think Bruce Berndt's Number Theory in the Spirit of Ramanujan (2006) may be along the lines of what you're looking for, and also possibly G. H. Hardy's Ramanu

I think Bruce Berndt's Number Theory in the Spirit of Ramanujan (2006) may be along the lines of what you're looking for, and also possibly G. H. Hardy's Ramanujan: Twelve Lectures on subjects Suggested by His Life and Work (originally 1940, but republished 1991/1999 by AMS with further commentary by Berndt). I'm not qualified to say for sure, as they get too hard for me pretty fast. :) [Some of Ramanujan's easier papers I was able to read (very slowly) for quite a few pages though, such as the one on highly composite numbers.]