I don’t feel that Buddhism rejects a sense of purpose in life, it offers its own unique perspective on purpose; the freeing of oneself from the cycle of samsara, and asks you to remain objective in your pursuit of meaning.
I also don’t feel that logotherapy rejects detachment, one is free to mindfully objective of the pull of purpose and meaning.
Together, I think they cultivate nuance and a balanced perspective on active engagement.
Creating serenity in the appreciation of the fleeting the nature of attachment, to purposes, and to meaning.