Cannot use 2 external monitors with Anker 778 dock.

That would require that you drop from 10 bits/color to 8 bits/color, by turning off High Dynamic Range (HDR=OFF). Then manually adjust the refresh rate down to 60 Hz.

if you can do BOTH of those, that drops the data rate down to 17.28 G bits/sec for each display, and then they could both fit on one ThunderBolt-3 or -4 cable.

despite what the Dock can do, You will never get more than TWO displays on one Thunderbolt cable on a Mac.

From a much older discussion about TWIN displays:

To determine display names and capabilities, your Mac uses something resembling "plug-and-play". It sends a query to the display, and the display responds with its name, its capabilities, including default and preferred resolutions, and its SERIAL NUMBER. The serial number is how the Mac uniquely tells TWIN displays apart.

<< The displays I have are TWIN displays (both the same make and model). >>

What we have seen here with TWIN displays, sometimes the manufacturers have been sloppy about what field contains the serial number. The Mac uses VESA standard, and if the display-maker does not supply the serial number in the expected field, the Mac can not tell the TWIN displays apart, and they 'swap around'.

Your displays have a design defect. Only the display maker can fix this defect, and would have to issue a display firmware update to fix it. You should attempt to pressure them to fix the defect.

As a work around, two different models or different makers will not exhibit this symptom.

Another work around found by users is buying a little stunt box that intercepts the EDID information and lies about what display is connected:

https://www.amazon.com/s?k=edid+emulator+4k

Additional background information:

The details can be seen using a Utility like SwichResX, which reads out the EDID information the Mac gets back from a query of the device for its name, capabilities, and serial number. In an earlier investigation a User found that the serial number was there, but NOT in the correct field, so the Mac could not tell TWIN displays apart.

Apple has not responded favorably to suggestions that they "accept whatever junk the display provides, whether it meets the accepted standard or not", but you can certainly ask again.

That 27GP950-B appears to be a 3840 by 2160 (4K) display capable of 10 bits/color HDR, using FRC to achieve that resolution at up to 144 Hz.

display interfaces include:

2x HDMI 2.1

DisplayPort 1.4

since the dock is a ThunderBolt dock, it has the bandwidth to carry one very fast DisplayPort signal up the the highest rating of the display. If input to the dock were limited to USB-C inputs, only up to 60 Hz could be supported.

The DisplayPort cable or cable/adapter required for this use runs at about 38 G bits/sec and should be certified to the DP40 or UHBR10 standard. These may be limited to 0.5 meter, maximum.

For HDMI, modern Macs 2023 and later directly HDMI connected can run at slightly faster data rate of 42.0 Gbits/sec PROVIDED you are using a certified ULTRA High Speed cable of modest length.

<< I think there is some sort of limitation with my dock. >>

You certainly DO have that restriction. Those displays are running at too high a resolution to run TWO displays on that One ThunderBolt Dock.

ONE of those displays consumes the ENTIRE bandwidth of a ThunderBolt-3 or -4 cable, leaving only a small amount for low-speed devices like keyboards or USB-sticks

There is nothing inherently wrong with your present Dock that changing to a readily available CalDigit Dock can solve. The data rate is just too high for the Thunderbolt-3 or -4 cable out of the Mac to run two displays of such high resolution at the same time.

Only a genuine Thunderbolt-5 dock, and a Mac with ThunderBolt-5 ports, can run any faster, and those are all newly introduced items that are likely to be more expensive and in short supply.

LG UltraGear is a family of displays with varying capabilities.

¿Which model-number are you using, exactly?