[Samsung Galaxy Note 9 Questions & Answers] 6thtry:
The hub's non-charging USB-C connection does not support display connection or power input. The charging USB-C connection is only for charging (power input), no data or display.

Results for: Using the hub, the hub powered from an external USB-C power source (say, laptop or another USB connection from a display), display connected with HDMI cable, phone charges itself from the hub, all combinations with following:

Note 9 exynos, Note 10+ exynos (both on latest official firmware)

Lenovo ThinkVision X1 (first gen), LG 27UD88-W, Dell P2415Q

In all cases, the available DEX resolution choices in the phones were following:

16:9

WQHD 2560x1440

FHD 1920x1080

HD+ 1600x900

16:10

(WQXGA 2560x1600 - nope)

WUXGA 1920x1200

21:9

(UWQHD 3440x1440 - nope)

UWFHD 2560x1080

The signal at monitor seems to be 2560x1440 even if e.g. 1920x1080 output has been selected, so apparently the scaling happens in the phone. Thus, blurry mess, no chance to do the nice 1:2 scaling at monitor. (However, the few times I managed to see the 1:2 resolution combination in other tests, the results were not impressive; I think Samsung's way of rendering fonts at FHD (at the text "zoom" settings I happened to be using) leaves plenty of room for improvement.)

If the external power is not connected in the hub's power-only USB-C input, the phone will power the hub, and will only do screen mirroring, no DEX. Weirdly enough, screen mirroring is done with 3840x2160 resolution signal on all the 4K monitors tested (i.e. phone scales it up from e.g. its 3040x1440 display buffer) (Edit: view is vertical, so it is actually doing downscaling from 3040 to 2160 rows). Though phones could be sending signal for narrower view, and monitors just state it as full 4K after they "pad" the sides with black area... no idea.

I also tested how the two USB-C capable monitors behaved with direct USB-C to USB-C connection from the phone. This was a bit of hit and miss. For some reason, X1 can't remember which USB mode its connection is set to (USB 2.0 hub with higher resolution display support, or USB 3.0 hub with lower resolution display support), so whenever the cable is connected, it first starts in 3.0 mode and low resolution, and there is a chance that the phone will not understand when the mode is toggled "on the fly" to allow higher resolution modes.

The LG has no such switch, so presumably it is offering the full bandwidth for 4K at all times.

On USB-C direct:

X1 and Note 10+: resolutions FHD and HD+, mouse didn't work after mode toggle.

X1 and Note 9: resolutions FHD and HD+, mouse works.

LG and Note 10+: resolutions FHD and HD+, mouse works.

LG and Note 9: resolutions all except 2560x1600 available (but didn't test all), mouse didn't work at first, but later worked...

I didn't test the Dell U3011 again, as I don't think anyone has such a (fine) prehistoric monster any more in active use. At least not with phones like Note 9 or Note 10+.

USB-C monitor cables used were whatever each monitor came with, for charging some el cheapo USB-A to USB-C cable I happened to find, HDMI cable was one that I think came with the Lenovo (for both X1 and LG testing), and HDMI cable for testing the P2415Q was some semi-no-name brand cable that I had tested long time ago to be good for plenty of things.