Part 1: EVs
The idea being that the system will keep me from overloading the 125a service by switching off power to the EV circuit if the backyard appliances are on.
I find it interesting that you're wanting to do that with the one load specifically designed to be able to do that. I mean, they put a lot of tech into EVs to enable you to do exactly that thing. Except better.
For the EV part of the equation, see this Q&A here.
Implementation wise, you need a $450 Wallbox Pulsar Plus from Costco, a cat5e "ethernet" cable, a $300 power monitor that goes inside the main panel, and that's it. The EV charging will automatically self-regulate so it doesn't overload your panel.
It will charge at full speed until A/C, water heater, pool and sauna all happen to cycle on at the same time, then it will reduce to 25 amps. If you then ALSO turn on a hair dryer, it will reduce to 12 amps. But it will not stop. And of course all those loads are unlikely to kick at midnight.
Emporia's unit can do the same trick but REQUIRES a $125 software upgrade and functioning 2.4 GHz WiFi at both panel and parking spot. No WiFi, it defaults to a very slow speed. Do not use an Emporia without the software upgrade, because without it, no WiFi = highest speed, which is not safe. It is not UL Listed as a result.
Before you go "oh noes, that's $750 and I already like my non-Wallbox EVSE", yes, you can get dumb load sheds that simply do a hard power cut to absolutely any EVSE (“charger”). They cost more than $750, because they're doing it the hard way - with a hard interrupt of 40A (arcing and degrading the contactor) and generally suck. If you are doing session based charging (e.g. authenticating with Bluetooth to serve as a anti-Karen Lock), any hard power cut will end your session and stop charging.
(Karen locks are to keep an over-entitled neighbor from plugging into what they have decided is a free public station. The Wallbox has a Bluetooth lock which does not require functioning WiFi. The Emporia has similar if the WiFi is up.)
Part 2: Everything else
My 125a panel is almost full in breaker slots and load capacity, and won’t support adding circuits for a few backyard appliances (hot tub, sauna, cold plunge)... I am wondering if it’s possible to have an electric panel that can dynamically disconnect or prioritize circuits depending on real time demand.
The SPAN panel will do that, but since you bristle at $10,000 for meter work, I'm guessing that's Right Out at about $8500 installed.
However, you can still get this functionality with "dumb" load shed devices such as SimpleSwitch, DryerBuddy and the like. These knock out one load when another one is pulling. Many of them are marketed for EV charging, but disregard that - as dumb switches they are inferior for EVs. But very fit for dumb appliances.
I covered that material in the above link. For a catalog of those, see Reddit's load management wiki. These are costly, but can effectively have one load pre-empt another (dryer pre-empt water heater, etc.)
However, you should note that two different devices both putting CT clamps on the service wires is not going to work. They will dynamically "fight each other", causing pulsing power on both. So don't use a Wallbox for an EV and also a DCC on a hot tub.
