What I did: I opened Geany (I'm sure that Geany was maximized). I changed the size of the sidepanel at about 50%, so 50% editor and 50% sidepanel. I closed Geany. I reopened Geany.
Result It was not any more 50% editor and 50% sidepanel. I tried it many times.
Then I did something like this: I changed the size of the window, then I changed the size of the sidepanel. Then I closed Geany. I reopened Geany. Then I maximized Geany. And now it works properly, so the size of the sidepanel is remembered after a restart of Geany.