I think inconsistent watering might be a candidate. If they get dry and then get a lot of water, they often split. The cure is a regular watering regime.
I don't think it's carrot fly damage, if you look at this link there's a photo of the damage they cause, and l don't think yours look like that. https://greensideup.ie/carrot-root-fly/ I think Gemma might be right and it's watering problems.
I’ve just looked at the rest and I think both carrot fly and watering may be the culprits some look like your photo Anni and the splitting may be additional Thanks though
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Sorry I can’t give you any advice for your next crop as I’ve never grown them.
https://greensideup.ie/carrot-root-fly/
I think Gemma might be right and it's watering problems.