The context here is extremely important. All of this (the invasion exercises, the missile tests, the Korean War) have taken place in the Korean peninsula. None of it has threatened the US homeland in a meaningful way.
In addition, the exercises have been going on since 1997. That's a long time before any missile tests were conducted. If the DPRK (North Korea's name for its state) had been testing nukes from Cuba in 1997 I'd feel differently. But note that even dropping live bombs on other countries is something the US gets to do without starting a war because the US military is so powerful. Very few other countries operate that way and North Korea certainly isn't one of them.
(Of course, the official North Korean propaganda is that South Korea doesn't matter, because it's merely a colony of Imperialist America, to be liberated by our brave northern brothers. How nice of them.)
> the exercises have been going on since 1997.
North Korea has been caught developing nuclear weapons as early as 1992, which led to it threatening to withdraw from NPT in 1993. It's a shitty situation with decades of history, and you could easily find plenty of things to blame on both sides. But interpreting it as the US threatening to invade NK is a pretty biased take.
It's "practicing invading North Korea" in the same sense North Korea's missile tests are "practicing dropping nukes on America." It's a war practice, all options are on the table, with the hope that they won't be necessary.
South Korea and the US had canceled the yearly joint exercise in 2019, hoping for a better relation with North Korea. It didn't work out - see https://en.wikipedia.org/wiki/List_of_North_Korean_missile_t...
The exercise resumed in 2022.