Today (2023-11-16), Enflo gave a talk about the invariant subspace problem at Valencia which one can watch on youtube https://www.youtube.com/watch?v=LXOAOY-NEV8
I did not get more insight than from his preprint on the arxiv. However, he announced to put a new version there, soon (and apologized for the delay).
Edit (2024-04-10). As Johann Langemets observed, there is eventually a new version of the manuscript: https://arxiv.org/pdf/2305.15442.pdf