If you believe in long term mean reversion of CAPE ratio for US stocks, you'd expect price/earning multiples to contract by a factor of 2, over some hard to predict time frame, where CAPE reduces from 38 back to about 20. If we arbitrarily guess that contraction happens over 10 years, that'd be -6.7% / yr for 10 years, from 0.5^(1/10). Then add the return components you mentioned from dividends and earnings growth.

One approach I've seen a few folks do is to fit a regression model of annualized real stock market returns over the next 10 years as some function of CAPE or 1/CAPE or log(CAPE).

It doesn't give a very good fit on training data, R^2 in the range of 0.2-0.3, i.e. it cannot "explain" most of the variation in 10 year returns.

CAPE based regression models like that have said the US stock market has been overpriced for the last decade! But investors in the US stock market have done pretty well over that period, with really good returns. Maybe these models are accurate but we've just gotten lucky? Maybe these models aren't very good. Hard to tell.

Elm capital publish estimates of expected returns of a few asset classes quarterly: https://elmwealth.com/capital-market-assumptions/

How do you plan to adjust for government actions that affect purchasing power of the currency?