From what you give, the difficulty on the network is changed after ~ 1.4 days (2016/1440 blocks per day). It can take longer or shorter than 1.4 days to adjust difficulty depends on how fast each batch of 2016 blocks found.
There are 144 blocks each day, not 1440. So the difficulty changes every 14 days.
The big difference is difficulty does not increase two times or halve like block rewards. Therefore I don't see why people care about how difficulty change around halving time. The miner capitulation or new participation makes more sense on difficulty changes.
The issue is the the halving may cause an large abrupt drop in the total hash rate, and blocks would take longer until the difficulty adjusts.
This year, the difficulty is nominally scheduled to adjust a week after the halving. Suppose that the hash rate drops by half (not likely, but not impossible). In that case, blocks will each take 20 minutes and the difficulty won't change for two weeks. Cutting Bitcoin's transaction rate by half for two weeks could have a major impact.