regarding the link to the Devonshire family Duchess Georgiana died in 1806, Duchess Elizabeth died in 1824. The next duchess was Louisa who married in 1892.

The 7th duke when 2nd Earl of Burlington was married to Lady Blanche Howard between 1829 and 1840. His father was married to Hon Louisa o Callaghan between 1807 and 1812. He was killed in 1812 and she died in 1863. His father was married to Lady Elizabeth Compton between 1782 and his death in 1834.

I think it’s just as likely to be a Burlington jewel, especially since Lady Elizabeth Compton was an heiress. The tiara and necklace look to be a marriage. The necklace looks a lot older maybe even eighteenth century or mid Victorian whereas the tiara is more like a late nineteenth century item.