3rd monitor not detected but system "reacts" when it gets plugged in

I recently tried adding a 3rd monitor to my machine (Ubuntu 20.04.1 LTS).

Right now my setup is two monitors: my laptop's built-in one (1080p) and an external 4k monitor on thunderbolt. It is set in extended display mode and with 200% zoom (else everything is way too tiny on my 4k).

Now when I plug in this new external monitor (1080p) on my only laptop HDMI, the system does register that something was plugged in: it briefly pops the "new display" choice bar: Extend display - Mirror - Single etc... And all my displays reset to 100% zoom from 200%. So at first it seems like it does detect a new display was added, but the display stays black and does not appear in the displays part of settings.

The new display also does not appear connected when I run xrandr:

Screen 0: minimum 320 x 200, current 5760 x 2160, maximum 16384 x 16384
eDP-1 connected 1920x1080+3840+0 (normal left inverted right x axis y axis) 344mm x 193mm 1920x1080 144.03*+ 60.08 60.01 59.97 59.96 59.93 1680x1050 84.94 74.89 69.88 59.95 59.88 1600x1024 60.17 ... 320x175 85.27
DP-1 connected primary 3840x2160+0+0 (normal left inverted right x axis y axis) 525mm x 295mm 3840x2160 60.00*+ 3360x1890 60.00 2560x1440 60.00 1920x1080 60.00 640x480 59.94
HDMI-1 disconnected (normal left inverted right x axis y axis)

I think my system should support 3 displays, especially since when I boot on Windows (dual boot) all 3 displays are working fine.

When I run: xrandr --listproviders

Providers: number : 1
Provider 0: id: 0x45 cap: 0x9, Source Output, Sink Offload crtcs: 3 outputs: 3 associated providers: 0 name:modesetting

When I run: lspci -v | grep VGA -A 10

00:02.0 VGA compatible controller: Intel Corporation UHD Graphics 630 (Mobile) (prog-if 00 [VGA controller]) DeviceName: Onboard - Video Subsystem: Micro-Star International Co., Ltd. [MSI] UHD Graphics 630 (Mobile) Flags: bus master, fast devsel, latency 0, IRQ 173 Memory at ab000000 (64-bit, non-prefetchable) [size=16M] Memory at 40000000 (64-bit, prefetchable) [size=256M] I/O ports at 5000 [size=64] Expansion ROM at 000c0000 [virtual] [disabled] [size=128K] Capabilities: <access denied> Kernel driver in use: i915 Kernel modules: i915
--
01:00.0 VGA compatible controller: NVIDIA Corporation TU116M [GeForce GTX 1660 Ti Mobile] (rev a1) (prog-if 00 [VGA controller]) Subsystem: Micro-Star International Co., Ltd. [MSI] TU116M [GeForce GTX 1660 Ti Mobile] Flags: fast devsel, IRQ 255 Memory at ac000000 (32-bit, non-prefetchable) [disabled] [size=16M] Memory at 80000000 (64-bit, prefetchable) [disabled] [size=256M] Memory at 90000000 (64-bit, prefetchable) [disabled] [size=32M] I/O ports at 4000 [disabled] [size=128] Expansion ROM at ad000000 [disabled] [size=512K] Capabilities: <access denied> Kernel modules: nvidiafb, nouveau, nvidia_drm, nvidia

An other weird side effect: when I disconnect the new non working display, the built-in display goes black. I then have to unplug and replug the 4k display for it to come back.

I didn't really find anyone with the same exact issue. Could it be an issue with my Nvidia driver? Any other commands / setups I could check?

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