I really want to pull you back from what looks like a costly path here. You are thinking of the load as a traditional "dumb" load, which necessitates giving it a fixed amount of power. Modern EV charging standards are much smarter than that.
This allows you to sidestep the 100A/200A question entirely, a question that I think will go badly. The only evidence I see is the metering equipment being rated for 200A, but that doesn't mean much - all metering equipment on the market today is rated 200A. Anyway, let's get back to the good stuff.
From your loads which you described, your panel is fully subscribed, with no room at all. So we go directly to EVEMS aka Load Management. This ignores traditional provisioning rules; that is, we're no longer treating the EV station as an entirely stupid load. For about $300 extra over the cost of a normal wall unit station, it adds a power monitor which dynamically adjusts EV charge rate so the house cannot be overloaded (at least, not by the EV).
It will slow EV charging if you heavily use all your electric large appliances at once; so don't do that if you really need peak charging in a narrow time window.
Suitable models on the market today include the Wallbox Pulsar Plus w/ separate power meter, or the Emporia Load Management bundle with special firmware specifically to do this, or Tesla's J1772 Universal Wall Connector with Neurio power meter.
Any of these companies can refer you to electricians who have been through their training course and are familiar with the equipment; most random electricians have never heard of it, and/or hate it because it threatens sales of VERY profitable service upgrades.
As far as building this, the EV needs a breaker protecting the 40A circuit, and it needs an enclosure in which to put the power monitor. That Siemens panel you were looking at would be just fine, honestly. Since the 40A circuit is under active load management, it's not 140A of load to the meter, only 100A. The 200A main breaker can be disregarded.
The only change I would make is, you have chosen the 4-space version of that panel to scrimp a couple of bucks. I would go with the 8-space version, because there are many marvelous things that are well suited for the other 6 spaces, including a generator interlock, a surge suppressor, and solar. None of those things add draw to the panel, so the 200A main breaker can continue to be disregarded.