Is "not the" read as /nɔ đə/ here?
No. The /t/ is there for most speakers, but it is not exploded, which means the listener does not clearly hear it. If you compare the sounds you hear in 'but the' and 'mother', you'll notice that that there is a very slight stop in the first as the tongue touches the alveolar ridge for the /t/ of 'but'.
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