As a native speaker: Generally no, but it depends.
The "t" in "Rat" is pronounced much harder than the "d" in "Rad" is. BUT: The more and more you go into the north of Germany, lets say Hamburg for example, they have a very similar pronouncing of "t" and "d". Both often sound very hard (more like an "t"). Whereas people in the south tend to pronounce both letters more soft, like a "d".
Please don't use "High German" in English to mean (some perceived) "Standard German". It's bad (and incorrect) enough to use "Hochdeutsch" in German, but "High German" has a specific meaning in English: https://en.wikipedia.org/wiki/High_German_languages and the dialect spoken in Hannover is not in fact a High German one.
Right, but that standard is more about the written standard language than about the language as spoken in Hannover. I know it's a trope that TV news announcers supposedly pronounce things like they are pronounced in Hannover, but that pronounciation is not a standard.
Says who? Not Wikipedia, which says that that's a regionalism and quotes sources. Where is the standard codified?
> What is the ending of the pronunciation of 'und' in your region? Is it 'd' or 't'?
This is a trick question: If I answer the same as you pronounce it, you'll say "see, it's standard!", and if I answer the other way, you'll say "well, it's not my fault that you don't speak Standard German™".
That said, it's 'd'. If anything, it's softened further and half swallowed to say something like "un'".
Why would there have to be a standard? My point is exactly that there isn't one that captures how actual people actually speak German. There is one for written German that everyone agrees on, but not for spoken German. And that's completely fine.
And coming back to the original Rat/Rad distinction, https://forvo.com/word/rat/#de and https://forvo.com/word/rad/#de do sound different. The second "Rad" speaker (from southern Germany) makes almost no 'd' or 't' sound at all, but the same speaker pronounces "Rat" with a very hard and clear 't'.
The "t" in "Rat" is pronounced much harder than the "d" in "Rad" is. BUT: The more and more you go into the north of Germany, lets say Hamburg for example, they have a very similar pronouncing of "t" and "d". Both often sound very hard (more like an "t"). Whereas people in the south tend to pronounce both letters more soft, like a "d".
But in general they are pronounced differently.