The default socket type is float, but I would like to set it into other types, as I marked in this picture :
How could I do that?
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Like node group inputs / outputs in the shader editor, the value type is defined at the time of creation, and can't be changed afterwards.
You have to first create a dummy link to force the type you want in the node socket. You can then relink the socket to where you want it to be linked to.
If there is an automatic cast available between the two types (for example a boolean True / False is equivalent to an integer 1 / 0), it will be converted automatically for you. Beware though at the moment I don't think there is a warning message if you try to link incompatible types (Example : link an integer to an object socket).
Note that you can change the default, min and max value of the sockets in the right hand side panel.