should I have bet at any point in the hand ?

[Guido]

https://upswingpoker.com/hand/?pokeit=124HeVfL9

solver says

preflop this is a raise 5% of the time and a fold 95% of the time ! (indifferent 1)

flop check 77% and bet small 23% of the time (indifferent 2)

turn check 100% of the time (no indifferent)

river check 100% of the time (no indifferent)

but betting pot (optimal betsize) has amost the same EV

if half pot were the optimal betsize (which is not) than you were indifferent EV wise between checking 62% and betting 38%

i am wondering why on river 1 pot isthe optimal betsize here ?