When I first open your file, and select all, it says "3 objects of type group". With nothing selected, it just says "nothing selected". But it's possible when you first opened it, something might have been identified as an image. I think you said you already had removed some contents before you've attached the file for us. And opening the PDF (which can contain both raster and vector contents) originally something might have been indicated as an image.
I'm assuming if it is grouped the ungroup icon will be lit up.
Hah! No, Inkscape doesn't have the AI (meaning artificial intelligence) type of features, which AI (Adobe Illustrator) has. Inkscape doesn't think for you! (Which I have to say, I'm happy about! How would any program know whether I intended to ungroup something that is identified as a group. Maybe I want to duplicate it? Maybe I want to add something else to the group, enter the group and edit one or all objects separately, move the group, convert to pattern, add it to another group. etc.? You see what I mean.)
The status bar gives you hints about what you can do next, depending on which tool you have enabled. But there's no AI.
Anyway, I'm glad you got the paths that you need