So I guess that this means that the 240A breaker for my drier is using both legs?
Correct.
Hot L1 leg to Hot L2 leg measures 240V, nominal.
L1 to neutral as well as L2 to neutral measures 120V, nominal.
And also: the way you explained that is that the top most breaker on the left side and the top most breaker on the right side are both on the same leg?
Correct. Both are fed from Line 1 (L1) bus, leg.
(And from there on all the way down the legs alternate in pairs of breakers.)
Example for illustration purposes only.
Single phase 240/120Vac load center with 200A main breaker
Note the turned out horizontal bus tie breaker connection tab that is part of the left and right vertical bus bars.
Circuit breakers plug on to the bus bar tie tabs.
The left vertical bus bar is Line 1 (L1)
The right vertical bus bar is Line 2 (L2)
Breakers Left side. ............. Breakers right side
Top breaker L1 .............................L1
................... L2 .............................L2
................... L1 ............................ L1
................... L2 ............................ L2
................... L1 ............................ L1
....................L2 ............................ L2
An so on to the bottom of the panel.
No matter where a 2 pole breaker is plugged onto the breaker connection horizontal bus tie tabs the load side of the breaker is 240V nominal.
Might be Top connection of breaker L1 and bottom connection L2.
Or it could be top connection of breaker is L2 and bottom connection is L1.
It just depends on where the 2 pole breakers are located in the panel.
.