Currently, restaurant reservations for the May 20 phased reopening are only available on OpenTable. Earlier this week, guests could book dining reservations directly via My Disney Experience for June 1 and later:
Now those same reservations have been pulled from the system:
Yesterday, it was announced that Disney-owned shops and eateries would reopen on May 27, however it seems they may still need to tweak the system to allow for limited capacity reservations. Other third-party restaurants, like Jaleo, have yet to announce a reopening date at all.