Endnotes begin on a separate page. Is there a way to create a numbered heading section at the top of the page, formatted something like this?
## References ##
Short answer: yes, but I assume you also want the recipe 
Since endnotes in Writer are what their name implies, the very last objects in the sequence, you need a way to insert text consistently at the beginning of the Endnote page. You must then manage in a way that endnotes are not the last objects in the document (although they’ll be the last objects in their sequence).
I suppose that your document is already typed. So, select all the text and Insert>Section. In the Footnotes/Endnotes tab, check Collect at end of section for Endnotes. OK
Put the cursor at the very end of your document, just before the first footnote and add an empty paragraph. Enter “References” and style it Heading 1. If you don’t want it to be numbered, with the cursor at start, press Bksp: this will remove the number and give you an unnumbered entry in the TOC.
While here, Insert>More Breaks>Manual Break to insert a “tuned” page break. Select Endnote in Page Style drop down menu to force a switch to the Endnote page style, just like Writer would have done with “standard” endnotes.
In principle, the horizontal separator line is removed. If this is not the case, you can modify Endnote properties in Footnote tab, but if everything is correct, endnotes are endnotes and not footnotes.
You can add any heading before your endnotes and even “ordinary” text paragraphs to preface your endnotes. You can even write additional text after the notes outside the section.
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After some experimenting: if you use the page style Endnotes for the endnotes text, you can enable the header there, change the top margin of the page, then enter your heading in the header. Make sure that you don’t have a check mark in Same content on left and right pages and in Same content on first page.
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