Looks like a type of Molex connector, but that's probably irrelevant because you'll struggle to find new downlights compatible with those drivers anyway. The majority of modern down lights have the drivers built in or permanently attached, so you would dump those drivers and wire the mains cable to the new ones.
Your primary consideration is going to be something that fits the same size hole really.
Something with a better moisture ingress rating than IP20 would be a good idea in a bathroom, usually bathroom downlights are IP65.
Aurora seems to be a popular and respected brand, although I don't have any direct experience of them. Screwfix and most of the major electrical wholesalers stock them.
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