In film music, dialogue, and sound effects work, the go-to plugin for transparent pitch shifting is Pitch-N-Time Pro from Serato. It’s been around for many years. It’s hideously expensive ($800), but it sounds really good. I bought it several years ago and it works very well. You should be able to get +/- 4 semitones without trouble. It has several algorithms to choose from, depending on the material and how far you want to go with it.
There is a first class way that doesn’t require an expensive plugin. It sounds as though you like the tape style pitch shifting in the new IRCAM tool. That Method, varispeed, is the easiest and best method for pitch shifting without artifacts, if it’s acceptable to have the length change at the same time as the pitch. It’s exactly like slowing or speeding up the tape you’ve recorded your sample on: sounds change pitch and duration simultaneously. There are no fft algorithms needed, and it sound great!