2020 MacBook Pro with external display wakes frequently from sleep issue

that LG 34UC88-B display appears to be a 3440 by 1440 display at up to 10 bits/color, similar to a 4K display with the bottom half missing.

interfaces include

2x HDMI 2.0 and supports Picture-by-Picture.

DisplayPort 1.2

USB-C

if this is an Intel Mac, it does not have a built-in HDMI port.

I suggest you try a high-spec USB-C cable (clearly marked at SuperSpeed Plus or USB-10 or 20) up to one meter, rather than the additional complexity of an HDMI adapter. The adapter also requires more power than a straight cable.

On closer inspection, it appears that display can provide a charge over its USB port, but it is only a USB-3.0 port and too slow for display data.

Re your adapter: if the adapter electronics "bulge" is at the FAR end (next to the display) that adapter/cable is too long for reliable operation. The USB-C portion should be ONE meter or shorter for reliable operation. Otherwise the display will drop out often, and the Mac will be forced to re-evaluate the connection.

...and am running in “clamshell” mode.

Does this still happen when you leave the lid open? There are some physical orientations in clamshell mode that can cause the computer to overheat, such as putting the closed computer vertically on a shelf with the hinge down, blocking important hot air exit points.

this is its interface panel:

The SS-USB symbol (SuperSpeed) says 5 G bits/sec, not fast enough for display data. The lightning bolt is shown on the port that can supply some charging power. Note that this is NOT a ThunderBolt™ symbol. The difference is that a ThunderBolt symbol has a small arrowhead on the bottom.