technically not a ‘psychology PhD’ but rather a PhD in computing sciences
Yes, technically. Realistically it's a (smooth) blend.
Will this impair my future applications to doctorate roles/psychology jobs requiring PhD’s
Ideally, shouldn't.
However, this might depend on which sub-field you want to narrow to.
Psychology and computing have a long history; symbiotic relationship in a way. The interrelationship goes for decades; kind of a century.
Crisscrossing or cross-carpeting seems natural; more like a norm, especially where they interface.
One area is cognitive which has shaped theories in computing (and information systems). Psychology has been used in CSCW/HCI, education technology, cybersecurity (notably human-aspect, cyber-skill/use); neuroscience, NLP/LLM/AI are not left behind.
The close-knit comes to fore in joint-degrees, for instance UCC, Ireland and Yale psychology and computing degree program.
HCI (Human-computer interaction) is essentially a study at "the region of intersection between psychology and the social sciences, on the one hand, and computer science and technology, on the other" (Carroll, 1997)
Ref:
Carroll, J. M. (1997). Human-computer interaction: psychology as a science of design. Annual review of psychology, 48(1), 61-83.
Sample application:
Mayer, R. E. (1981). The psychology of how novices learn computer programming. ACM Computing Surveys (CSUR), 13(1), 121-141
Young, K. S. (1996). Psychology of computer use: XL. Addictive use of the Internet: a case that breaks the stereotype. Psychological reports, 79(3), 899-902