Hints: Ministry of Word Searches
Getting started:
These are word searches, but they’re not entirely conventional. However, it seems like the same nine words keep appearing all the time…
Finding a minimal grid:
You don’t have to be perfect to read the message, but it may help to know that you can fit all of the words on a single row, column, and diagonal. The Chinese remainder theorem might be helpful.
Extraction:
Graham’s Number ID is not accessible using the puzzle applet, and nor is any grid that exactly matches it, so you’ll need to make your own. See https://oeis.org/A240162 for help doing this.