Hi ARC,
The first two messages (#pragma message "CACHE READ COMPILED" and #pragma message "SYSTEM DEFINE NOT SET, DEFAULTING TO USER ROM") are normal, and are simply information messages about the compilation of the core files for the Oak. You can safely ignore them.
The actual error message that is causing your problems is the last one - "Cannot run program "/home/***/.arduino15/packages/digistump/tools/esptool2/0.9.1/esptool2" (in directory "."): error=2, No such file or directory". It appears that file file is missing...
Try navigating to that folder ("~/.arduino15/packages/digistump/tools/esptool2/0.9.1"), and see if it exists, and what is there. If you are using the 1.0.6 release of the Oak Arduino package like I am, you'll find that the esptool2 binary is actually one level deeper in ~/.arduino15/packages/digistump/tools/esptool2/0.9.1/0.9.1 ... move it up one level, and it should be fine. It looks like it was nested one folder deeper by accident on the latest update.
I'll open an issue on the OakCore github. I t seems to be be a bug that exists on Linux, not on windows, as I'm pretty sure I updated my windows build to 1.0.6 the other day, and didn't have any issues.