This hasn’t been confirmed by Southern or London Overground, but it appears that from Saturday 4th July, with the reopening of pubs and restaurants that they’re going to attempt to reintroduce a normal service.
Southern: 2 trains per hour to Victoria reintroduced, 4 trains per hour to London Bridge (currently two). Normal peak service on weekdays from July 6th, which means that the current East Croydon through service reverts to off-peak.
London Overground: A full service of 8 trains per hour to Highbury & Islington, 4 to Crystal Palace and West Croydon.
These changes haven’t been confirmed as when there was a plan to bring back a more regular service on the Overground, this was cancelled due to social distancing measures at New Cross Depot. Hopefully this may have been resolved?