The hard part is predicting rates.
You just laid out a relatively straightforward ( and IMO) likely case for rising long-term rates. However, the bond market is often not straighforward. Your second paragraph lays out a scenario that is less likely IMO, but plausible.
“And how does all this affect REITS ?”
That’s the simpler question IMO. As an investor, would I rather own an apartment REIT spitting out a NET after expenses 8% or would I rather have intermediate-term bonds paying 5% ?
What about if these same bonds went to 9% (apartment reits are much less attractive), what about if bonds went to 3% (more attractive for 2 reasons, cost of leverage goes down, relative value goes up.)