Hi all, I have fixed my problem but I am not sure which of the two following things I did actually rectified the issue as I did them both at the same time.
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Outdated NVDIA driver see https://knowledge.autodesk.com/support/revit/troubleshooting/caas/sfdcarticles/sfdcarticles/Background-3D-preview-is-grayed-out-in-Dynamo-1-3-2.html
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DirectX 10 for Dynamo 2.7 and below → download Download DirectX End-User Runtimes (June 2010) from Official Microsoft Download Center
Also, I did not realise the problem was fixed as I expected the 3D toggle button to appear right after the actions stated above, but I actually had to go to View > Background > Available Previews to see that the 3D background preview is no longer greyed out.