David it took some time, but I managed to get the correct data for you using the TIN Interpolation Tool. However, there is a catch. During my research I came across this article from September 2019 on Github where somebody had the same problem having e+ values using QGIS 3.8.3.
In this article the statement was made:
The extent of the output and the pixels size are likely to not match
perfectly, so there must be some rounding......
So I started testing your shapefile and your Tiefe NN seemed 162.600. But it constantly returned 1.79769e+ 308. I used the layers extent. When I exported it as a .CSV file it created an error. When I exported it as .XLSX and imported it again, the Tiefe NN was not 162.600 but 162.599 (with really a lot of extra decimals). So I created a new attribute field with one decimal, and my first test returned fine as you can see. I tested the most southern part (1341 features).
So your initial question, your raster was invisible and the values impossible, is solved.
But now your real problem. When I expend the test with more points (1809 features) this result was returned.
The reason for this is also explained in that article.
To honor the pixel size (ex. 0.25) the tool could simply round the
xmin/ymin coordinates DOWN to the nearest whole pixel size and the
xmax/ymax UP to the nearest whole pixel size. When doing this manually
through the extent parameter, the values are not honored. Padding with
extra pixels (rows/columns) is not possible either.
However, this new problem does not really provide you with a satisfying solution. But there is hope. Two days ago a new comment was placed on this article by Alexbruy with following link and title:
Fix calculating raster size in the TIN and IDW algorithms to maintain accurate pixel size
Here it is stated that the issue was fixed and is added to the Qgis 3.14.0 milestone. On the QGIS.org website it is stated that 3.14.0 is planned to be released on the 19th of June 2020.
I hope that this would solve your problem completely.
In the following wetransferlink I have the shapefile that I made from your original shapefile. Instead of using Tiefe NN use Hight (I know it is Height in proper English).
[Later EDIT by GISGUILD]
Since I understand that you need the data I made a Interpolated TIN raster for you in ArcGIS PRO. I will add this raster to the Wetransfer link. Simply browse to the RASTER folder and drop the entire tin raster folder in QGIS.