everything I'm reading is projecting rising interest rates for a while.
Then that expectation should be built into CD rates. In other words, the market's expectation of the change in interest rate in 2 years should make it an indifferent decision to buy a 2-year CD now and another 2-year CD in 2 years versus buying a 4-year CD now.
So the only difference is how rates actually rise relative to those expectations. If they rise more than expected, then you'd be better off buying short-term investments and reinvesting when they mature. If they rise less than expected (but still rise), then you'd be better off locking in the rate for a longer time.
If they rise exactly as expected, then it will make no difference.
Your math on the expected future rate is pretty close. The formula would be
(1+r(2,2))^2 = (1+r(0,4))^4 / (1+r(0,2))^2
Meaning the square of the expected 2-year rate 2 years from now is the current 4-year rate to the fourth power divided by the current two-year rate squared.
Evaluating that equation yields an expected 2-year rate in 2 years of 2.80%. If you think the rate will be higher than that in 2-years, then buy the 2-year CD. If you think it will be lower, then buy the 4-year CD.