I think you should reevaluate your very concept of "official", high detailed source for all country borders worldwide. OpenStreetMap data comes close to a worldwide dataset with acceptable level of details for many use cases - however, in each case, this must be evaluated critically.
"Official" sources for borders
For a ...
GEE does have a quite a few datasets involving climate variables. I'm listing a few datasets that may be of interest to you on there:
ERA5 - ECMWF Climate Reanalysis
Reprocessed GLDAS-2.0: Global Land Data Assimilation System
CFSR: Climate Forecast System Reanalysis
Beyond these remote sensing datasets, you'd probably have to look at getting monitor data ...