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The confusing part is, that $M$ basically is simulated on its own encoding $\langle M\rangle$. Nevertheless, I would claim its decidable by simply creating the following $TM$ $T$:

check if $\langle M\rangle$ is correctly encoded
Build a $TM$ $M$ with input $\langle M\rangle$
Simulate $M$ on $\langle M\rangle$ for $32$ steps
if $M$ halts, $T$ accepts, otherwise $T$ rejects.

This is totally straightforward, thus I am quite unsure. Any hint is highly appreciated!

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    $\begingroup$ this looks correct $\endgroup$
    – nir shahar
    Jun 28 at 13:07

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