On the early e2008 there is a known fault where it fails to charge on a rapid charger, no indication as to which type by Peugeot (It’s the Instavolt chargers), but that should not be affecting cars built after around last September onward & is curable with a firmware update by the dealer if you tell them it has failed to initiate a Mode 4 Rapid Charge they should look at the Service Bulletin and follow the instructions. As for a dealer knowing what you are talking about then that’s pot luck, my dealer doesn’t seem to know about Service Bulletins & tries to palm me off with excuses… so go to another dealer.
With a rapid charger what normally happens is you plug in the CCS connector when it instructs you then it goes through a series of checks to make sure it has a good connection, you hold the CCS handle until it finished the checks & starts charging. The older 50kW Polar chargers indicates the whole checking procedure & then comes up with the SoC % and indicates that it is charging, a GeniePoint will show little as they are triple headers where two sessions can be supported rather than just 1 and it only has a single display. Oh, I have come across a new e208 driver who didn’t know about taking the rubber cap off the DC ports so they could use CCS rapid charging, they were found on a 50kW rapid using the tethered type 2 cable & charging for a very long time… I explained to them how to expose the DC & use the CCS to get the rapid charge, but this is common on the forums with new EV drivers. The trouble is they block the charger for others.
For slower type 2 charging I’d suspect the charge cable, check that all the pins inside the plugs are straight. When you plug into a post charger or your home wall box, the cable should lock in at the car end & the indicator lights at the car end should indicate outside green flashing to say it is charging. Also, if you plug into a PodPoint post you need to confirm the charge with the App else it will stop after 15 minutes (the post chargers at Tesco etc), the post chargers at Asda & Waitrose are activated by a Polar/BP Pulse card, etc.
The App does have the option of Immediate charge/Deferred charge and you can set a schedule that is sent to the car, so maybe that is where your problem is. Mine is always on Immediate & I’ve never altered it as I use the OHME charger to charge it at home when the cheapest rates apply (all the scheduling is done by the OHME app & smart charger).