I think the 'today' is significant. It is not a long enough period to warrant a progressive form Also, the presence of the 'anything' gives an idea of completeness that does not go with a progressive form.
'I haven't been eating (much) recently/for several days' sound fine to me.
Incidentally, 'I haven't slept well in the last two days is acceptable. The progressive form simply emphasises the duration , and therefore the effect on you, of the non-sleeping.
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