It appears you have wired the new thermostat correctly. How long does the blower run before the condenser kicks in? How long are you waiting between attempts of lowering the thermostat temperature in order to start the condenser? What might be happening in the new thermostat is the the G terminal is energized immediately which turns on the blower, and the Y terminal has a delay and energizes after a period of time. On most furnace control boards the Y terminal also turns on the blower. So as an experiment try disconnecting the G terminal and then lower the thermostat enough to turn on the AC. The blower and condenser should turn on at the same time. The clunking you hear is probably the condenser contractor closing. I don't see how changing the thermostat would affect the noise level.

Not sure I followed it either. Depending on the model, the orange/blue connections on the ecobee are usually the reversing valve connection for a heat pump. Are you sure this isn't the case for your installation? In any event. follow from the connectiors at the thermostat/furnace/condenser and don't assume the colors are as they should be.

The Rh is to power the thermostat for heating, and the Rc is the power for cooling. Since this is a cooling only application, you only need a connection to the Rc terminal. Do not connect the old R wire from the wall to either of the adapter wires. You need to disconnect the old R wire from the Rc terminal, and connect one of the adapter wires. The other adapter wire goes to the C terminal. The old R wire could be connected to Rh without the jumper, or keep it disconnected and cover the end with tape so it cannot short to any other wire. I recommend you keep it disconnected and covered. If that does not work, then you may have to install the jumper between Rh and Rc. Consult the Ecobee installation manual about the wiring for applications that are cooling only.

Two different homes, two different models. You should be sure what your own system's needs are, as to available wires and compatible stats, before moving forward. They're not all the same. Ask your HVAC guys - the two I dealt with were more than happy to install Honeywell units because, as I said, they're the gold standard. Honeywell makes several of the private label branded stats too, the ones that the equipment companies sell with their own names on them. In one, we have two Honeywell Vision Pro 8000 series REDLINK units, because of the need to have a wireless connection from the thermostat to the furnace and AC equipment when we did a complete equipment replacement and added AC. Honeywell's REDLINK system may be the only one that offers the wireless thermostat to equipment communication but maybe not. It also offers WIFI and so internet user communications with all the normal kind of apps and even from a PC over the internet. We've had them over 5 years and the performance has been flawless and reliable. . At the other house, also with a complete furnace and AC equipment replacement three years ago, we put in one Honeywell 9000 series WIFI thermostat. The same with it too, consistent competent service. Because we split our time between these two places, it's a regular thing for us to access the stats remotely to put one in the equivalent of "away" mode, and to switch on in advance the one we're coming to. No issues ever (except for the few rare times an ISP system is down and so the the stats aren't accessible) . I know that Honeywells generally are compatible with heat pumps and aux power systems but do check in advance about what you have to be sure.