Hello, If this affects only one user, then check what "Permission Set(s)" they are assigned on the User Card. It should be enough with just BASIC Permission set which contains Insert permissions for table 2000000096 "API Webhook Notification".
However if this is Online, then the user may have "Permission Set" "D365 BASIC", and this only contains Indirect Insert permissions for the table. Indirect permissions must be supported by adding permissions also on whatever object is trying to do this insert, which is a code change.
If you add one of the following Permission Sets to the user, then they all contain Insert permissions to the table: "D365 BUS FULL ACCESS", "D365 BASIC ISV", "D365 BUS PREMIUM" or "D365 FULL ACCESS". Or compare permission sets with other users who do not have the problem.
There is a permission trubleshooting page called "Effective Permissions". Run that for this and for other users, and filter on "Object ID" = 2000000096 and see if the users do have different permissions, and if they do then compare what Permission Sets are different.
I hope this helps?