Speaking as somebody with 20 years of international egov experience. Why is there an egov minister? There is no weird separate “electronic government” that’s somehow distinct from the “real government”. What typically happens in these scenarios is that the “egov people” are given a bunch of money to go play with in the corner while the grownups continue with business as usual. Also, having engineers that high up in the hierarchy is not sustainable. Come next elections, he is going to be out, and very likely all his reforms and changes will be undone by the next person. Just look what happened to the GDS in UK.
The engineering responsibility should be low in the hierarchy with wide political support across all ministries. Unless the ministry of social affairs sees, that the only sensible way to fulfill their mandate is to offer electronic services and is also able to execute that, nothing will get better in that area. The egov minister might walk back and forth the government meeting room on his eyebrows but he will not be granted the power to tell other ministries how to do their jobs.
A position represents an area that the government wants to focus on. That area may look more like vertical or horizontal integration. In this case it'd be horizontal integration, where an eGov is a function of all other aspects of the government, but also requires a common approach in terms of infrastructure, engineers etc.
You can think about it like object orientation (vertical) vs. functional programming (horizontal). Both have their use cases.
The drawbacks you're concerned about are resolved through communication. If there's ongoing communication, there will be synchronization.
The actual title it "Ministry of electronic governance" and there's also a "Ministry of effective governance".
These look like ministries introduced to address specific concerns or goals of the leadership. When something is "ministry of something" gets budgets and freedom to use these budgets and other tools that may not be possible if it was just "department of something under the ministry of other thing".
When Turkey used to be friendly with EU and had a goal of joining the EU, there was "Ministry of EU".
The engineering responsibility should be low in the hierarchy with wide political support across all ministries. Unless the ministry of social affairs sees, that the only sensible way to fulfill their mandate is to offer electronic services and is also able to execute that, nothing will get better in that area. The egov minister might walk back and forth the government meeting room on his eyebrows but he will not be granted the power to tell other ministries how to do their jobs.