This is because the MPs of Bhagalpur and Munger have not written any letters to the Railway Ministry recently proposing the Bhagalpur Delhi Amrit Bharat Express. Only the Nawada MP, Vivek Thakur, is interested in it and only for the Nawada area. As per the news received, the Eastern Railway is not interested in maintaining any Amrit Bharat Rake in any of its CDOs like Howrah, Bhagalpur, Sealdah, Kolkata, Malda, Asansol, etc. So the matter is forwarded to other zones and SER for running the Amrit Bharat train from Kolkata and other ER terminals. As a result, Bhagalpur LTT proposed by CR, Bhagalpur UDN proposed by WR, and SER proposed ABs from SHM/SRC to SMVB, TEN, TBM.

Now, talking about the future of the Bhagalpur Delhi Amrit Bharat Express, at least one MP, either Lalan Singh of Munger or Ajay Mandal of Bhagalpur, should write around 2-3 letters to the Railway Ministry for running the Bhagalpur Delhi Amrit Bharat Express. Now, if these MPs don't do anything, then we all know the behavior of ECR and as a result, ECR may run the Gaya Delhi Amrit Bharat via KG line only to satisfy the Nawada MP. So, my advice to the people of Bhagalpur/Jamalpur is to make your MP active in this matter and therefore 2-4 letters should be written by the BGP MP or the MGR MP alongside staying active in Railway-related matters for it. Otherwise, the Bhagalpur Delhi Amrit Bharat Express via KG line seems impossible.

I am predicting non-conformity.

As I have said earlier, either the HWH-BGP line gets extended to Jamalpur or crosses the Munger bridge. That doesn't mean extension up to Barauni.

As you are worried about the timetable and resting time at Bhagalpur. Changing the timetable of Vande Bharat is not a big issue, as we have seen with earlier Vande Bharat.

Example - Bhopal Jabalpur Vande Bharat extension with a changing timetable.
Indore Bhopal Vande Bharat up to Nagpur.
Gorakhpur Lucknow Vande Bharat up to Prayagraj.