Index edit page crash after upgrading Drupal 10.1

Those methods don’t exist yet, as far as I can see. Did you maybe apply the patch from 📌 Define 'original' as property on the entity object Needs work ?

Yes, One of the other contributed module using that patch.
Is there any other way that we can define those methods in search api itself.

Once the Core issue gets merged, I’ll add the methods to UnsavedIndexConfiguration. Before that, you’ll have to add them manually to your local copy.