There`s no such thing as a "happy belated birthday"
There`s either "happy birthday" ON the birthday
or nothing at all.
If people were honest enough they would instead have said:
It was your birthday yesterday/last week/month. I`ve completely forgotten about it because I don`t care enough.
Next year I will:
1. Either set notifications because I clearly would still not remember
2. Stop talking to you to avoid the awkward "I`m sorry I forgot your birthday thing".
So it`s plain simple. Either you remember people`s birthday and wish them on the day.
Or you stop giving a damn and live happily ever after.