Works for me:

<img width="631" alt="Screenshot 2024-12-19 at 15 07 19" src="https://github.com/user-attachments/assets/96f10eb7-6ca7-4cde-bde4-592e8b6c4bae" />

The currently opened project is greyed out so you don't re-open it by accident but selecting the other project works and it gets opened.

I don't notice Projects -> Close button is available, so this means the project is already opened. Geany will not close the project when I close it, so on the next start of Geany the project is still open.

This is weird, project closing works for me.

It also works for me. I said I don't notice that the Close button is available (that means there is an open project). This is my mistake.