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
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)
Carroll, J. M. (1997). Human-computer interaction: psychology as a science of design. Annual review of psychology, 48(1), 61-83.
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