Clearly I am long overdue for some inbox cleanups!
Some context: the field has a long-running conversation regarding how much weight to put on measures below the global measure, and whether the domains are sufficiently robust to interpret. So keep in mind that the most psychometrically sound measure is, all other things being equal, still the global one (the FSIQ on the WAIS/WISC/WPPSI family of instruments). This is not by accident, btw, as the original author set out principally to obtain a good measure of g. The indexes emerged in stature later, mainly through the work of his successors (notably Kaufman, who is best known for his work on the WISC-R and -III).
That being said, there is data to support the four domains identified by the WAIS-IV, although there are, again, ongoing discussions about what they actually consist of. Some are more obvious. VC has pretty good general consensus that it mostly is related to verbal reasoning, but with overlay effects from an individual's access to rich langauge sources over the course of their history. It seems to be reasonably predictive of language-based achievement, for most people (e.g., reading, writing, communication)--but not everyone. PR appears to be mostly related to nonverbal reasoning, with a heavy visual component. It seems to have some connection to mathematical achievement and mechanical skills.
WM and PS are a bit more ambiguous, mainly because a lot of different attributes or conditions can affect them. For example, WM can be lowered by attentional dysregulation, such as that found in persons with ADHD or other executive function challenges, but it can also be affected by emotional interference. And some people do well on WM but not on other measures of memory, or vice versa. We do know that tasks in this category are often reflective of a person's phonological loop, which is the length of sequential auditory information that you can hold in short-term memory, prior to transferring to long-term storage. A longer span turns out to have significant correlations to strengths in acquiring fluent phonetic reading skills, as well as in math achievement.
Here I'll throw in an example of a divergent profile that might be familiar to some readers: persons with high VC and low WM might (not always, as there are other factors too) be among those who are quite strong in oral language and comprehension or expression of complex verbal reasoning, but struggle to learn basic reading or spelling skills. Sometimes they can discuss topics at a high level, but generate unexpectedly simplistic written language.
PS likewise has many possible pathways to lower performance (which is why clinical observation and interpretation by a skilled professional are important). A lower score might result from fine-motor difficulties (the physical act of generating the responses efficiently), or visual perceptual difficulties--especially tracking, or decision speed, or anxiety/perfectionism, to name a few. WAIS's PS can also be described as clerical speed, to emphasize that not a lot of reasoning is involved in it. There are some other speed tasks that involve other skills, such as various types of retrieval fluency measures (verbal fluency, naming items based on a provided category; naming fluency, naming images of familiar items or symbols, computational fluency), with or without the fine-motor component.
Whatever PS is truly measuring in an individual person, it does appear to have some patterns of need areas. When it's not mainly motor speed, weaker performance in this area does sometimes appear to play out in real life as difficulty keeping up with the pace of interpersonal interactions of various kinds, both academic and social. They may be able to descrie appropriate social reasoning and perception in the hypothetical, but find that the speed of real life passes them by before they are able to read and respond to social situations.
Your own profile includes some qualities not assessed in much depth on the WAIS (e.g., verbal flexibility). I would submit that the challenge area in flexibility (what we call "shift") may be more impactful than the slow speed itself. And the way you've phrased it suggests that the low PS is a symptom or result of the low shift, not a cause. It may be helpful to learn a collection of clear but socially-acceptable verbal requests for wait time, so you don't feel rushed when you are generating a communication. For example, "I'm thinking," "give me a moment," "let me give that some thought," "I'm going to give that the time it deserves." Or you can buy time for adapting and processing by reflecting what you've heard back to the other conversational partner: "So what I hear you saying is..." "If I understand correctly..."