Every generation uses this. I had a 60-year old coworker who said this to me when she was training me years ago.
https://books.google.com/ngrams/graph?content=you+got+this&y...
No doubt there are older people who use the phrase today, but that's still more annoying; they are the older people who are very proud of inserting 'cray cray' and 'yeet' into conversations.
Those people are just delulu.
A similar phrase is 'I need you to', which appeared around the same time. Eg: 'Okay, I need you to calm down' or 'I really need you to be supportive right now', etc. To my ears it sounds gratingly self-entitled.
“Mark had enough of his job, so he stood and yeeted his laptop out of the window.”
At least yeet can be funny if you're referencing a meme/being intentionally ironic. I'm not sure there's another great word to replace it anyhow, chuck or hurl are probably the closest but don't imply the level of reckless abandon, and aren't quite as "multi-purpose" in terms of understood contexts.
If it's not a quirk, then it is probably due to one usage of the words (eg: "So you got this angry customer, see?") peaking in the 1940s, and a different usage (eg: "You can do it... you got this!") rising in the 2000s.