It seems most define the halving as the time when block 840000 is found.
However, as soon as block 839999 is out, miners will be working at a halved subsidy, as they will then be working on block 840000. The halving therefore really happens at the time when block 839999 is found.
The timing of block 840000 is merely a weak indication on whether the network survived the halving.
Also, the halving countdowns I see have a countdown that counts down one second at a time. But the expected time of the halving increases by one second for every second that a block is not found. The countdown should therefore be rather static, only counting down by ~10 minutes each time a block is found.
At time of posting, block height is 839976, 23 blocks to go until block 839999. At a current average of 9.8 minutes per block, the countdown is at 3h 45m 24s. Estimated time of actual halving: 2024-04-20 00:37 UTC.