Where does “palaeoswamp” come from?

palaeoswamp (English) comes from English swamp, from Middle English swam, from Old English swamm, from Proto-Germanic *swammaz, from Proto-Indo-European swombh- — sponge, tree-fungus, swamp.

Ancestry of “palaeoswamp”, step by step

Step	Language	Word	Meaning
1	English	swamp	A piece of wet, spongy land; low ground saturated...
2	Middle English	swam	swamp, muddy pool, bog, marsh", also "fungus,...
3	Old English	swamm	mushroom, fungus; sponge; first/third-person...
4	Proto-Germanic	*swammaz	—
5	Proto-Indo-European	swombh-	sponge, tree-fungus, swamp

Every word from Proto-Indo-European swombh- →