The NGREEDIA 4050 Laptop only has 6GB VRAM and is also much slower than a 4060 Laptop, maybe think about paying for a 4060 Laptop (the next big jump would be a 4080 Laptop, not 4070 Laptop). Unfortunately AMD dGPUs use a less advanced TSMC node (N6) and lack in efficiency vs NGREEDIA (TSMC N4) (this is a full node improvement), which is kinda important in mobile hardware/notebooks.
More info regarding the HDMI issue: Supposedly a vBIOS (video BIOS) (BIOS of the dGPU) update can increase the HDMI 2.1 bandwidth from HDMI 2.1 FRL4 (32G) to HDMI 2.1 FRL5 (40G). But I don't know if this works for the new 2023 models and the product warranty is probably going to expire.
NOTEBOOKCHECK, can you check which HDMI 2.1 bandwidth this notebook has? Previous models were supposedly HDMI 2.1 FRL4 (32G).
More HDMI infos:
Assuming this LENOVO Legion Pro (AMD version runs longer than the INTEL version assuming everything else is equal btq.) offers HDMI 2.1 FRL4 (32G).
Gaming in HDR on OLED TV
Assuming the OLED TV doesn't require a 4K120Hz signal to allow HDR, 4K 4:4:4 chroma 10bit and up to 104Hz is be possible. Personally I think I notice quite a difference on my OLED TV in fast titles (CS:GO custom 64 player servers) of 100 Hz vs 120 Hz, but since this dGPU is not for 4K gaming, one should be able to reduce the resolution to 1080p/1440p and still have enough HDMI 2.1 bandwidth for native 120Hz 4:4:4chroma and 10bit for HDR gaming.
Watching HDR videos on OLED TV
In theory this would be enough to drive an OLED TV with 10 bit (10 bit are required for HDR), native/normal 4:4:4 chroma and 60 Hz, as the required HDMI 2.1 bandwidth for this is enough:
15.68 Gbit/s (15.678432 -> 15.68) <- ((3840+80)*(2160+62)*3*10*1*60)/10^9.
* 3 means there are 3 subpixel (RGB) per pixel
* 10 is the color depth in bit per subpixel (10bit are required for HDR)
* 1 means full/native 4:4:4 chroma (for 4:2:2 use 2/3 and for 4:2:0 use 1/2)
* 60 [Hz]
* +80 and +62 come from the CVT-R2 timing format
But the question is if the OLED TV would allow for HDR at 60 Hz setting (I'd assume it would?), or if it requires the full 120 Hz?
But the bandwidth would not be enough to drive a OLED TV at its native 120 Hz:
32.27 Gbit/s <- ((3840+80)*(2160+127)*3*10*1*120)/10^9.
100 Hz would be possible, however, but this would be a weird value and 60 Hz are not divisible without a remainder, this means there may be screen tearing.