The bottom right thumbnail thing really bugged me and confused me when it came out, because I always just want the screenshot on the desktop right away, as it used to be. I don't know why they couldn't have the delay/thumbnail AND put the file somewhere I could reach it immediately. But IIRC, there is some setting that disables the thumbnail behavior and lets the file be written instantly.
Funny, I never want the screenshot saved to a file and I literally never look at the desktop. I either use ctrl to store the screenshot in the clipboard or want to use marker tools and then copy the clipboard. This new flow was an improvement to me.
I use a trackpad exclusively with MacOS. If I want it immediately on the desktop then I can just "swipe away" (to the right) the thumbnail and it skips the pause.
Not perfect but I do value being able to edit it from there, or right click and save to clipboard. So it works for me.
You can also just drag it to the right.
For me I want it to hang around longer actually. I will take the screenshot I want, open up mail or messages or something to dump it there. Right as my mouse is hovered over it and a milisecond before I can click it, it jumps away. I've resorted to sometimes giving it a partial drag which resets the counter while I am still getting situated over to wherever the screenshot is going.