Bitmaps are the most inefficient way to store images, they use no vectors for same colour/hue/whatever spaces its just pixel by pixel. Anyway that’s beside the point. The is no background tab on format/page
If you expect any answer at all, edit your question to mention you OS and LO version. This is a start. Also, in which format do you save your file (.odt or .doc(x))?
Then describe your goal in document writer/author/designer words (not technical or procedural terms). After that, tell us what you did (which menu, command, … you used) to attempt to achieve your goal and what you got instead of your expectation.
Please, press edit below your question to add more information. Add Answer is reserved for solutions.
By the way, in Format Page, you would not find background but Area; and PDF is not a image format; it is a container format.
Open the pdf in Draw, select the vector image, in menu click File > Export... In the dialog that opens Save as Type .svg , tick the box that says Selection, and Save. In Writer menu click Insert > Image..., navigate to your saved svg file, select it and click Open.
BTW, jpg image compression does take into account similar hues in the patterns that it applies to reduce file size. Using Insert > Image... and choosing a jpg will include the jpg in the Writer file, as opposed to just pasting the image which will add it as a png.
Did you copy and paste from pdf? probably pasted as bitmap then. Did you try Dragging the pdf into Writer or using Insert > Image…? You might need to right-click and select Crop to hide extraneous space/items
I highly recommend using the Writer Guide as a reference source