Welcome to the forum
Cold engine
Take radiator cap off, should be full to the top if there are no leaks
Start engine
Watch coolant at cap opening
Should not be over flowing, might have on "burp" on start up then no flow in radiator at all, coolant should just sit there
If it starts to over flow then yes, looks like a blown head gasket or cracked head
A cylinder is pumping "air"(exhaust) into the cooling system, displacing coolant in the heads and pushing it out the radiator cap opening
If coolant just sits there then no bad head gasket or head
Water pump bypass may be clogged or blocked
Water pump bypass is also know as the Heater Core, lol
The heater hoses send coolant from upper intake(thermostat) to heater core(firewall) and then another hose brings it back to water pump
This needs to be clear passage of coolant
If outside you can take off both heater hoses and put a garden hose on the heater core and flush it out to see if there is good flow, in both directions
And just a heads up, you should swap heater hose around at the firewall every 2 years when you change coolant, that reverses the flow thru it and will help it last longer
Are water pump and fan spinning the right way, serpentine belts can be install backwards on water pump pulley so way less cooling
Bad thermostat, yes new, but YOU are the one testing this new part, so if its a bad part................
Regardless you need the shroud but not your issue