In that, and Allah knows best. Is reciting Ayat al-Kursi part of the shaykh's adhkar?

As for reciting Ayat al-Kursi and the morning and evening adhkar, yes, it has been mentioned regarding them.

There are some narrations about it, but we say that what is established after the prayers is more authentic.

It is more authentic in the adhkar after the prayers, but at bedtime as well, there is evidence for it, and the evidence is in the adhkar after the prayers.

And at bedtime, it is more appropriate than what has been reported about it being from the morning and evening, so we say that it does not appear.

To say it in the morning and evening, but it is said at bedtime and also after the prayers, and Allah knows best.