Product Safety Testing - EU
I think the best aproach is indeed to look into EU law (like you already suggested):

https://europa.eu/youreurope/business/selling-in-eu/selling-goods-services/selling-products-eu/index_en.htm

which (regarding safety) links to

https://europa.eu/youreurope/business/product/product-rules-specifications/index_en.htm

which links eventually to (only) CE marking.

Regarding those other logos: they're likely certifications for other regions (FCC for USA, CSA for Canada etc) or logos for product identification (e.g.Class II lasers) etc.