“Elastique” time stretch algorithm by zplane (0) seems to be a common choice by plug-in companies. Their C++ library is pretty straightforward to use, and most importantly it sounds good.

Generally speaking, phase vocoder (1) algorithms are what you’d want for developing your own pitch shifting algorithm.

[0]https://licensing.zplane.de/

[1]https://cmtext.indiana.edu/synthesis/chapter4_pv.php