As the documentation shows, you can inject the Unix time into the build system by writing
build_flags =
-D CURRENT_TIME=$UNIX_TIME
You can use this timestamp to convert it into a human readable time.
Alternatively and way more easier, use the __DATE__ and __TIME__ built-in macros that are compiler-defined and are already strings (https://www.cprogramming.com/reference/preprocessor/DATE.html).
While the project name isn’t directly available, you can pass in $PROJECT_DIR (string escaped) to get the full ptath to the projects, e.g., C:\Users\Max\temp\atmega4809.