Connecting up the SMA coax adaptor to the modem, switching over to the external antenna on the Huawei modem without mounting the Yagi did give me a signal but not a very strong one.

Wireless Statistics Before
RSRQ: -10dB
RSRP: -116dBm
RSSI: -87dBm
SINR: -1dB
One bar
Speedtest: 8.85Mbps download, 55mSec ping, 0.99Mbps upload

Wireless Statistics After
RSRQ: -5dB
RSRP: -112dBm
RSSI: -83dBm
SINR: -11dB
Speedtest: 9.79Mbps download, 55mSec ping, 0.99Mbps upload

(speedtest is limited by the ISP's speed throttling).

A little bit of a difference, but now I have the modem mounted inside the house not high up outside next to the roof for the best signal (which was never a long term proposition). I also have 6m of RG213 cable which has a loss of about 3.5dB as well as a RG213 connector and SMA adaptor likely I'm losing another 1.5db there. I think the internal antenna in the Huawei wireless modem is pretty decent because the modem box size is large and with the high LTE frequencies the ¼ wave size is only 32mm so certainly possible to have a decent internal antenna in the unit.

The speedtest tells me the radio link quality isn't the limiting factor both before and after, it is hitting the Vivid throttling first. The slight speed variation from before and after is likely the tower / net congestion.

This means my Yagi is getting about 7dB better than the internal antenna which isn't bad and unless I have made an error in the calculations or assembly it is about as good as you are going to get. My Yagi is designed for 12.5db of gain from 2300Mhz to 2400Mhz with 50 ohms impedance at those frequencies (so no special impedance matching needed). The Yagi is designed to use a normal dipole (not folded) and a Pawsey stub to convert from the balanced dipole to the unbalanced coax.