Other than general frothiness in the housing market, there are very few similarities to the Great Recession. NINJA, 0 down, and liar-loans aren't really a problem, and there isn't a broad trend of people cash-out refi'ing to fund lifestyle.
I live in Boise, one of the Zoomtowns that experienced rapid appreciation during the pandemic. There's been a lot of hand-wringing about a pending crash for the past several years, but that hasn't really happened. We declined a bit from the peak of 2022Q2, but the trend is now flat with seasonal fluctuations.
It's not just that people are locked into sub-3% loans, though this is part of it. Those that bought near the peak are engaged in loss avoidance (sunk cost fallacy) -- they do not want to "lock-in" losses by selling, which would mean losing a big chunk of their down payment. People have real skin in the game with 20% down, which makes it difficult to short-sell or walk away.
Millennials are a large cohort that is now entering the prime home buying years, and there's an ongoing persistent housing shortage in much of the US. Broad based inflation in materials and labor is adding to the difficulty and cost of producing more housing.
Counterbalancing this, the long-term demographic outlook for the US is negative, which should eventually reduce demand for housing.
Instead of trying to predict the future, I've found Scenario Planning really useful in these situations. The idea is to write out a number of possible future outcomes and your personal pros and cons of each. It's just a way to help structure your thoughts and think through various implications. I did this before we moved from CA to ID and found it very helpful as we basically came to the conclusion that we really didn't like 3/4 potential outcomes, and the one outcome that was acceptable was very unlikely and even if it happened it would take too long to be meaningful to us.
For this specific question you could do something like a 2x2 along high vs. low interest rates and high vs. low housing supply. We are currently in high interest rates and low supply. Then consider low supply and low rates -- yes, this would likely trigger higher housing prices, but lowering rates may also make equities more desirable as bonds become less attractive and people chase higher returns. High supply and high rates would suggest stronger downward pressure on RE prices, whereas high supply and low rates would be somewhat similar to the current situation, but could put upward pressure on equities. Fill in as many details as possible, think through the implications, then consider how you feel about these potential outcomes. You may decide it's not worth holding on to a rental if even if you miss out on some near term gains. Or you may decide RE investment is worth the risk for you even if it doesn't perform as well as other assets.