I can only assume that the intention of both the short two-way cycle lane and the relocation of the crossing is to provide better facilities for the cycle route from Catford to Peckham. This is currently mapped to go via Bartram Road as you’ve described, which is a detour. The proposals would see it linked straight into Eddystone Road and over the railway lines.
The fact that the cycle lane is two-way is so that riders from Sevenoaks Road van avoid the right-hand turn into Brockley Rise and use the toucan crossing instead. It’s not intended for and won’t be used by cyclists riding down Brockley Rise.
At first glance it looked a bit daft to me too but once you’ve looked at the cycling network it kind of makes sense. The one issue I see is the housing development on the corner which is going up at the moment. Will it still fit?
As for mixing with pedestrians on the footway, agree that this can cause issues, but this is quite a short stretch so speeds shouldn’t be high and it also isn’t exactly a busy cycling route.