I've made a couple of websites for early/mid-career professors.
As with many website projects, there was consultation needed in the "What does the client want?" stage. Like you, they wanted something to match the "industry standard" for people in their position. So we did some research. I looked up a few dozen professors, PhD candidates, and postdocs in their field and from their institution and took notes. I also looked at specific institutions and specific professors they mentioned.
In general, the existing sites were more formal than casual (except in photo choices), they absolutely all included a CV given its necessity in job-hunting, they were mostly simple in design, and more than half were a single page. The younger they were, the more they tended to have interesting designs. I may also have imagined that the young were more formal, not yet feeling the freedom to play and risk seeming unserious. Many of the clunkiest were the highly limiting templates provided cheaply or freely by the institution, but sometimes those were better than what the person might have come up with; some people had evidently learned basic HTML circa 2001.
WIth this information, one of my professors decided to match the majority fairly exactly, and the other to just slightly one-up it. Neither wanted to stray too far from the boundaries we'd researched, turning down more modern features like a dynamically filterable list of publications.
One quick frame challenge for you is that I'm not sure if by "personal webpage" you mean to distinguish it from a professional one. Only one person in my research had two sites, and it was confusing, particularly since the content was largely the same, so it was hard to tell which was more up to date or authoritative. There's no need to divide your web presence unless you have a hobby to share that's totally unrelated to your work. If the goal is to make you findable by other researchers and institutions, make it professional.
And finally, let me draw your attention to my earlier "in their field" and "from their institution". You can add "at your career stage" if you like (or not if you want to be aspirational). My findings may not match yours when factoring in those things. I suggest you spend a couple of hours skimming a bunch of academics' websites taking notes on what's there and how it's presented. Find out what's appropriate for where you are, and set that as your baseline. If you find that 10% of people in your position put up a CV, leave it out. If 90% of them include it, start making yours presentable. And bookmark the sites you find most effective.