This has always been difficult to understand for me. How is the second futures contract valued in relation to the front month contract? My understanding is there are carry considerations (3 more months of carry for basis) and there is basis switch price involved. However, in a world of prolonged low volatility and low nominal rate levels, basis switch is a thing of the past. So is carry be the main driver for calendar spread? Then assuming the same CTD, a long calendar spread position would be short front month basis and long next futures' basis.

Trading bond futures calendar spread is actually a very involved exercise, with many moving parts. But first things first, recall that bond futures price is approximately: $$F = \text{spot price} - \text{carry} - \text{delivery option value (DOV)} \pm \text{rich/cheap}.$$ So calendar spreads represent the differences in spot prices, in carries, in delivery options, and in the relative richness/cheapness.