I'll take a stab at this one.
Cap rates are a representation of how bullish investors are on the future of a given market sector. If all the fundamentals look good and risk is low, cap rates will be low. Low cap rates are like Blue Chip stocks meaning that investors will take lower returns because the assets have a good, low-risk, long-term outlook.
Cap rates in multi-family have been driven down to absurd levels long before interest rates started to go up. On a Marcus & Millichap multi-family market call a few years ago, they were already joking that 3% is the new 4% in this sector. These cap rates have been below interest rates even when you could get commercial loans at 4%.
That means that, in the past few years, a ton of cash has moved into this asset class. Cash doesn't have exposure to interest rates. From personal experience, I know a bunch of investors who ramped up in the early 2010's and needed to scale from flipping and buying small rentals by 2018. Because they already understood tenants and toilets, multi-family was a logical step into the world of commercial RE. Likewise, most people understand housing and might participate in syndications and other vehicles when alternative investments appear less attractive. Or they just want a piece of the real estate appreciation train.
Another reason that we are still seeing activity in multifamily is the cyclical nature of real estate and the associated lag time. There are lots of projects that were earmarked (and underwritten) before interest rates started climbing. It makes more financial sense to be somewhat upside down on them than to abandon them altogether and lose the sunk costs. Most of these developers have good balance sheets and can wait out the current cycle. Remember that the developer's exposure is not market value of the project, but only their cost. So if they go into a project with 50% financing with 25% cash and 25% profit, the performance may be pretty manageable even with higher debt service.
All the metrics show that we are still short on housing. So there has been a massive flight to multifamily projects pushing cap rates down to a point where it doesn't really make much sense. But remember that rents and residential property values have basically doubled over the last 5 years. If this trend continues, buying at a 3-4% cap rate now and betting that a 5 year loan reset will be back into the 5-6% interest rate range, you'll be right side up with leverage again.
But that's very speculative and very bullish...which is the short answer to your question.