BASED ON MY THOUGHTS
The words 'annihilated’, ‘destroyed’, and ‘does not exist after death’ that you quote refer to ‘body perish at death’. Because it is impossible to use the word ‘cessation’ for ‘body perish at death’ (because body will disintegrated, destroyed, annihilated, not cessation of body), so, the word ‘cessation’ is more appropriately associated with ‘being or non-being’ (because it’s non physical as body) or it refer to the words that you quote → 'rejoice in (the idea of) non-being ’ or we can say it ‘rejoice in cessation of non-being’
Bhikkhu Sujato translated it like this in the Diṭṭhigatasutta
And how do some get stuck? Because of love, delight, and enjoyment of existence, when the Dhamma is being taught for the cessation of existence, the minds of some gods and humans are not secure, confident, settled, and decided. That’s how some get stuck.
And how do some overreach? Some, becoming horrified, repelled, and disgusted with existence, delight in ending existence: ‘When this self is annihilated and destroyed when the body breaks up, and doesn’t exist after death: that is peaceful, that is sublime, that is how it is.’ That is how some overreach.
Based on his translation, the words ‘annihilated’, ‘destroyed’ refer to ‘self’, not physical ‘body’. This is easier to understand, and I feel more precise. Even though I realized I had to cross-check it again with the original text.
I hope my words can help.
Please correct if there is something wrong.
Thankyou 