The car is very sensitive to the sort of driving you do and the length of trips as far as economy goes. Most of my trips are short, so most are done entirely or almost entirely on battery.
The car does about 12 miles on about 5kWh in summer, about 8 in winter, so whether it pays to use electricity is something you can work out, depending on what you pay for fuel and electricity of course.
Say worst-case. 8 miles, 15p kWh. Petrol is what, 115p litre? (Not sure as I last put some in the car last March.....I kid you not. It still has just under half a tank left in it).
On a run, lets say it does 45mpg.
So a gallon costs 522p and gets you 45 miles, so 11.6p per mile
Electricity gets you (worst case) 8 miles on 5 kWh, so 8 miles on 75p or 9.4ppm
Best case, it goes down to 12 miles on 5kWh so 6.25ppm
Varys a lot on what you pay for power though. I'm soon to switch to Octopus Go, which if you charge the car at might is 4p kWh. I'm mainly doing this as I have a Tesla Powerwall so I'll charge that up at night then run the house on it during the day. Certainly wouldn't bother if I only had the C350e to charge!
Your call if it's worth it or not, but it'll take a while to pay for an outdoor charging point at those rates if cost is the sole driving factor for you.
The one thing you really don't want to do is drive the car in CHARGE mode - that drinks petrol, makes loads of noise and hurts performance too.
I've never used a public charger as they are generally way too expensive for charging a PHEV with a small battery, as the ones I have seen all charge on time, which is a bad deal for us. If it's free, then great of course.
The car can only charge at a maximum of 3.6kW, which is only slightly faster on a Type 2 than the granny charger, which is limited to a maximum of 3.2kW (?) IIRC. That said, I wouldn't want to use the granny charger on full power - when I did use it before getting the fixed unit I limited it to 10A to protect the socket form overheating.
I had a 7.2kW charger installed as I fully expect to have a full EV one day.
An example of a short trip beyond battery range, I did a 40 mile round trip the other day starting with full charge and it returned an indicated 63mpg. Have to add in the cost of the charge as well of course.
This time of year, the pre-entry is almost worth the price of admission on it's own! Sadly, that joy is very quickly offset by watching the battery range plummet as you drive down the road.