"Fossil" originates as "obtained by digging", and refers to any mineral resource so obtained. Transferrence to "fossilised remains" (as in dinosaur bones, wood, plants, etc.) is secondary.

1610s, "any thing dug up;" 1650s (adj.) "obtained by digging" (of coal, salt, etc.), from French fossile (16c.), from Latin fossilis "dug up," from fossus, past participle of fodere "to dig," from PIE root bhedh- "to dig, pierce."*

Restricted noun sense of "geological remains of a plant or animal" is from 1736 (the adjective in the sense "pertaining to fossils" is from 1660s); slang meaning "old person" first recorded 1859. Fossil fuel (1833) preserves the earlier, broader sense.

<https://www.etymonline.com/word/fossil>

I'll note that the 1833 date for "fossil fuel" predates establishment of Standard Oil or its predecessors by four decades.