Regarding CAPE values and affect on sustainable withdrawal rates, Kitces has done some good research and has several interesting articles on the topic, including
Shiller CAPE Market Valuation: Terrible For Market Timing, But Valuable For Long-Term Retirement Planning. Mad Fientist I believe attempts to distill much of those articles, including the affect of valuations on his page
Safe Withdrawal Rate for Early Retirees. The latter is a good article, but I think it is worth digging into the original Kitces work, though it is time consuming. This thread is long and I don't remember the contents, so sorry if this has been posted already.
It has been sometime since I read Kitces work on CAPE and withdrawal rates, but from what I recall, they have some predictive value over moderate (10 year time periods) but neither short nor long time periods. The MadFI page has a tool (sign in required) that lets you estimate an updated withdrawal rate based on current CAPE values.
It's interesting work, but I didn't see anything that would make me immediately change my plans. The time periods are too removed for me to think of it having immediate actionable consequences, but you can draw your own conclusion. I think it comes to the advice mentioned earlier:
The key points of the trinity study are that saving 20-30 times your annual expenses should result in your stash lasting 30 years.
When it comes to portfolio theory it should be as simple as stating that a diversified portfolio (across asset classes and within asset classes) is a good idea. It's also a good idea to utilise a stock heavy portfolio because the no 1 risk to portfolio failure tends to be inflation which stocks protect against.
Based on these points a portfolio of 50/50 through to 90/10 (international stocks/domestic bonds) that is 20-30 times your annual expenses means that you have placed yourself in a statistically likely position for your retirement to be a success from a financial perspective. That is the best that you are going to get. Trying to mimic the best past performance or protect yourself perfectly is not possible as we can't predict the future.
The past can only offer broad general principles to follow. It can't offer completely detailed mathematically exact criteria to follow.
If it brings you joy to save 20x your expenses and retire, do it.
If it brings you joy to save 30x your expenses and retire, do it.
(Similar for anywhere between 20x-30x)
If it brings you joy to save less and retire, I would say be cautious and hesitant, but it's your life.
If it brings you joy to save even more and retire, I'd say you saved a lot, good for you, no harm done and it's your life.
The cautions about your personal rate of inflation, or misunderstanding your long term expenses are good ones and worth noting, but they fall out of the realm of what can be answered with historical stock and bond returns.