The three links in the PDF work OK for me on W7.
I moved the Impress .odp file to C:\Users\John\Desktop and created the PDF. The first two links point to the "equivalent location" on my PC, the third points to archive.org.
I get the same values for the links irrespective of whether I tick or don't tick
Export URLs relative to the file system in File > Export as PDF > Links.

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Editing an already inserted hyperlink was surprisingly tricky. I needed Help which says
Editing Hyperlinks
When you Ctrl-click a hyperlink in a Writer document, your web browser opens with the requested web address. If you don't use a mouse, position the cursor inside the hyperlink and open the context menu by Shift+F10, then choose Open Hyperlink.
Change the text of a hyperlink as follows
- In Writer documents, you can click anywhere into a hyperlink and edit the visible text.
If you leave the hyperlink by positioning the cursor somewhere else, only the visible text will be changed.
If you leave the hyperlink by entering a space character directly following the last character, the AutoCorrect - if enabled - will change the target URL to be the same as the visible text.
- In all document types, you can open the Hyperlink dialogue box to edit a hyperlink. First set the cursor into the hyperlink or directly in front of the hyperlink, then click the Hyperlink icon on the Standard bar.
Change the URL of a hyperlink as follows
- Option 1: As described above, open Hyperlink Dialogue Box.
- Option 2: Open Hyperlink Bar (View - Toolbars - Hyperlink Bar). Click on the hyperlink, do not release the mouse button and drag the hyperlink to the Hyperlink Bar. Edit the URL on the Hyperlink Bar and press the Return key.
Change the attribute of all hyperlinks
1. Open the Styles and Formatting window.
2. Click the Character Styles icon.
3. Right-click the "Internet Link" or "Visited Internet Link" character style, and choose Modify.
4. In the dialogue box, select the new attributes, and click OK.
Edit a hyperlink button
If the hyperlink is a button, click on the border to select it, or press the Alt key while clicking. Open the Properties dialogue box through the context menu. You can edit the label text under "Caption," and modify the address in the "URL" field.