I've got close, but not quite there.
- Paste the vector into a spreadsheet in LibreOffice
- Upload the spreadsheet to Google Drive
- Copy the vector object
- In the other sheet, Insert Drawing
- Paste the object, but it pastes as a bitmap instead of a vector
Alternatively, follow steps 1 and 2, and then transfer the contents of your other sheet into the uploaded one and accept that you can't add any more vectors to it. You might have luck downloading the Google sheet as an ODS file, adding your vectors in LibreOffice, and uploading it back to Google again, as long as all your sheet content is compatible with LibreOffice.
I got this working. The trick was to upload the ODS sheet to Google Drive, and then open it using Sheets and copy the tab into the sheet that you want to use the images in.
2022 Update: Unfortunately this is no longer working! As soon as I open the ODS file in Google, then the vectors are just low resolution bitmaps.