Should I greet my ex boyfriend a happy birthday?

my boyfriend and i is taking a break from our relationship a week ago. lack of time issues. Long story short, he got a new job with hectic schedules and i become clingy. he said im stressing him out, so i decided to give him space. Currently, w'ere on no contact phase but his birthday is coming tomorrow though, i dont know if i should greet him or not. i dont want to look clingy again and i want as much as possible to show him that my life goes on without him. not an ego issue, i just dont want him to worry about me. he love me he made that clear to me on our last talk. its just that he can't handle the pressure that i have given to him. should i contact him tomorrow and greet? ... please excuse my English. im not a native English speaker
Should I greet my ex boyfriend a happy birthday?
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