Already tried simple USB phone to laptop and Samsung SmartSwitch, but they also need the phone unlocked.
I'll take it to a shop soon, but I am OTT untrusting of randos having access to my stuff.
Took my phone to shop and it will cost €90, which does seem like a lot but I had decided that if it was under €100, I would pay to repair rather than buy a new one (tempting because this one's 4 years old!). But my phones are not expensive and I didn't even pay for this one myself. Fingers crossed!