I have inserted an image into a page in Writer. I want the image to fill the page and the text to jump from the previous page to the next.
I have expanded the image as much as possible but there are still four lines of text. When I drag the corners to make the image bigger it springs back to the current size.
This is extremely difficult to achieve reliably. How is your image related to text? It will usually work when the image can be completely “detached” from text (sort of DTP job – DTP = desktop publishing). It also requires the use of a dedicated frame style.
So, OS name, exact LO version (don’t say “latest” which is meaningless but something like 25.8.3.2 or, better, paste the result of Help>About LO) and save format. Note that the need to use a frame style implies you save .odt.
What is your experience with styles?
I’ve discovered that the problem was I had rotated the image after inserting. If I insert an image that’s already the correct orientation I can make it the right size.
Version: 24.2.7.2 (X86_64) / LibreOffice Community
Build ID: 420(Build:2)
CPU threads: 8; OS: Linux 6.8; UI render: default; VCL: gtk3
Locale: en-GB (en_GB.UTF-8); UI: en-GB
Ubuntu package version: 4:24.2.7-0ubuntu0.24.04.4
Calc: threaded
Writer is not an image processing program. It offers very basic adjustment possibilities. But due to remaining bugs, it is much better to prepare the image outside Writer so that the image is inserted “as is” without any scaling, cropping or clipping.
Why is there a rotate function? If it doesn’t work then it should be removed.
You can use the rotate function but when processing the text file the rotation of the image always has to be done. Maybe in some situations this is too cumbersome for Writer. So accept the advice to do these actions (rotating images) before inserting an image into Writer.
For creating pages fully covered with an image I could recommend the other method via menu Format | Page Style … For that you need an extra Page Style in your case. IMO these pages are stabler than pages with inserted image (frames).
More information:
https://help.libreoffice.org/latest/en-US/text/swriter/guide/pagebackground.html
Hopefully the function will improve in future. Meanwhile additionally use brain.exe. 
This solution works fine when your images have deterministically predictable locations like a frontispiece page before chapter start. It is easy because text ends at a definite position at end of previous chapter and starts after a break (materialised by a page break, frontispiece page and new chapter heading) in the new chapter.
OP is asking for something more elaborate: insertion of an image without interrupting artificially text flow. The image should simply be ignored; text ends at end of a page, skips the image page and restarts on the other page. And if text is edited, text should reflow without leaving empty space.
The only way I know to handle the case is to attach the image at some absolute page. And IMHO this should be done only in the latest phase of document development when we know approximately page distribution. However for it to work properly, the whole document must be strictly and thoroughly styled, without direct formatting, because image insertion will cause huge reflow. And, as usual, direct formatting is a layout serial killer.
That is Bug 115934 - Bad position for rotated images (use unrotated image position values)
The current workaround is to rotate the image in another program.