The EV charging unit is called an EVSE. It is not a charger, it's a smart GFCI that tells the car how much current it can draw. The EV world is full of costly misconceptions about EV charging. Those commercials with the unicorn and tooth fairy don't state the half of it. I want the one with the tentacle monster who think they need cord-and-plug connection, or the faeries who think they need a 50A circuit. To correct many of these I always link this place in this video.
The reason for the rule
To my understanding, my main service panel is 125A with a breaker of 100A. My subpanel is 100A. .... The solar design says: max breaker calculation: 125A * 1.2 - 100A = 50A and they plan on installing a 35A breaker.
Yes, that checks out because of your 100A main breaker.
Why is that rule that way? Because without a limit, you might have 100A of utility power and 100A of solar power, feeding 200A of loads on a 125A bussed panel. NEC says if the solar and utility breaker are on opposite ends of the bus with the loads between them, you can push the bus limit by 20%. The "main breaker in the center" is granted an exception but still, the major loads need to be between main and solar breaker! If you can't do that, then you're stuck with bus limit and main+solar must <= 125A.
Since loads must be in the middle, I'd expect your solar to be placed at space 15-16 and your 100A feed breaker to be moved to spaces 13-14. I hope you have the feeder length for that; this is the folly of cutting the wires as short as possible. The surge should go to 7-8, with the 15A breaker to 6, and the heat pump and EVSE should go in 9 through 12. Or be double-stuffed if that panel supports quadplex and the loads don't need GFCI. A hard-wired EVSE never needs GFCI, it is a GFCI.
Alternately, you could replace that interior subpanel with a much larger panel, and move a lot of stuff there. What's most important to be in the all-in-one is daytime loads that would benefit most from solar.
Fitting more loads
First, a +30A service upgrade is cheaper than you think: all it'll cost you is a gas stove and a bit of plumbing lol.
If you watched that video you know charging an EV off a 15-20A 240V circuit isn't a problem. Some people might prefer more but they don't need more. (let's face it, if you're driving 200 miles you'll pass a bunch of DC fast chargers, and you'll be stopping anyway for bathroom/snack; simply coordinate them. They take about the same amount of time.)
Another option is that 30A general-use, receptacle circuits are regulated like 15-20A general-use receptacle circuits: no limit to number of receptacles, and you're left to your own recognizance to not overload them. Thus a dryer and a plug-in EVSE can be on a 30A general-use circuit.
They also make "Load shed sensing EVSEs" that will put a clamp meter on a circuit or the service, and back off EV charging to keep a circuit or the service from going over. Really we're going to see A LOT of tech like that in the near future become very affordable. Power companies are going to force it to happen because it then enables incentive-based demand side management, which is cheaper than peaking plants.
On the heat pump, I can't guess at sizing. The original gas furnace takes a minor amount of power for the air handler, and you'll still need that if you reuse your duct system.
Heat pump water heaters are something of a swindle. They pump heat from the utility room into the water, thus causing the utility room to become an icebox (which then hurts their efficiency). So you need to run the furnace harder, which means you're really heating the water with gas. Or resistance electric if you stick baseboard or space heaters in the utility room, only now your efficiency is worse! It's only a benefit if you can scavenge that cold blast to air condition your home.
Also since they air condition the utility room, a heat pump water heater needs a condensate drain. In theory they will have an emergency drain for the overpressure safety valve, but an emergency drain can route uphill. A condensate drain cannot.
Much more interesting to me is the fact that split heat pump systems can support multiple heads in multiple rooms. One of those heads could be a hot water tank! So now your heat pump water heater has the outdoor unit actually outdoors where it needs to be. That makes sense.