What does 'offline' mean on my Thai visa exempt stamp?

It means as you enter Thailand your big brain goes offline and the small brain below goes online.

As normal. 60 day's on arrival and can extend after that for 30 more days.

What is the safe entry thing?

Its just Thailands subtle hint to turn the phone off , disconnect and have an absolute blast. Go to Thailand and get Offline ... 😉

System was down when you entered.

Yes last month+ the immigration system had a lot of updating (offline) timings 🤷🏻‍♂️😅

No panic, they couldn’t input your entrance to immigration system. Most probably computer system was not working.

I had to do some digging on this, but was able to get information from Tod in the other visa group.

The day that you entered, the immigration system was having issues. The "offline" written at the top of your stamp means the computer was offline when you entered. What that specifically means is unknown. Maybe your entry is not in the computer? Maybe it will be entered at a later date so the date might not match your stamp. The handwritten offline is to explain whatever discrepancy might result from this. It's not anything for you to worry about, and everyone who was entering at that time also had that written at the top of their entry stamp.

Guessing their computer was offline...

Probably means that their system is offline