What does my ex-boyfriend mean when he says Happy Tanabata to me?

The first possibility is that he just wishes you well and hopes you can find something better and be happy. The second possibility is that he still can't forget you, but because he has broken up, it's hard to make it clear, so the implicit saying of Happy Tanabata is actually to attract your attention and want to make up with you. The third possibility is that he is just a symbolic clockwork message, wishing you a happy holiday, which has no substantive significance. The above is my analysis, which may not be accurate, but I hope it can help you. Of course, if you feel good, you can also use it.