It doesn't look like they can apply (in my case) ToU split rates to the meters at the moment, so unfortunately the cost breakdown visible on your IHD will be incorrect, but the kWh power usage is correct.
What I can suggest is downloading the Bright app (from Hildebrand / Glowmarkt, who are approved suppliers) with access to the raw meter data via the DCC. Once you've registered your meter on the Bright app you can view your power usage (the costs will unfortunately still be wrong as they pick the tariff rate off the meter)
However, you can now log into your account on the Glowmarkt website and download the raw meter data in CSV format which can be loaded into Excel, then apply your tariff rates to the half-hourly energy usage to calculate your costs.
The “Act Tariff Price” register on the meter shows 29.94p per kWh
The data polled from Glowmarkt contains the half-hourly energy usage in kWh, and also the epochTimestamp (the current local-time in BST or GMT) and the base UTC dateTime. However it doesn't show the tariff rate applicable for that particular period. I used this to show the epoch in human-readble format
https://www.epochconverter.com
epochTimestamp, kWh, dateTime, Epoch coversion
1656543600, 0.039, 2022-06-29T23:00:00.000Z 30/06/2022, 00:00:00
1667259000, 0.030, 2022-10-31T23:30:00.000Z 31/10/2022, 23:30:00
1667260800, 0.031, 2022-11-01T00:00:00.000Z 01/11/2022, 00:00:00
Looking at the calculations in the “Bright” app…
The Bright app only shows a single tariff rate of 29.947p per kWh
So when the Bright app calculates the electricity costs it must be polling the meter for the half hourly usage in kilowatt hours.
Since Glowmarkt/Bright does not know anything about the customer’s account, it can only be getting the rate by polling the meter for it.
This means that it's cost calculation can only produce the energy cost based on the single unit rate of 29.947p
It therefore can not calculate the cost between midnight and 7:00 a.m. based on the cheaper overnight rate.
So thinking about the way the IHD must work…
This must interrogate the meter for the daily/weekly energy usage in kWh. To calculate the corresponding energy cost it has to multiply this by the rate in pence. If the only rate it can pull from the meter is the single unit rate value, the IHD will never be able to display the correct cost information for a multi-rate tariff.
Looking at the way the EON Next app shows the energy usage costs…
At the moment this must be doing exactly the same as the Bright app ie polling the meter for the energy usage and the tariff rate, since the daily cost it currently displays is virtually identical to the Bright app.
However since EON does have access to your account information, surely the app must be able to poll the meter for just the half hourly usage data, and then apply the correct rate for the specific time period with the relevant rate it knows from your account details.