yes, I use it with a screen this size without any problems

Yes, application with this resolution without problems

Can only give technical details and unfortunately no answer whether the graphics card supports Ultra Wide monitors with 3440 x 1440 pixels?
Processor graphics ‡ HP Pro Mini 400 G9
Intel® UHD Graphics 770 (generation unknown)
Base clock frequency of the graphics
300 MHz
Max. dynamic graphics frequency
1.50 GHz
Video output
eDP 1.4b, DP 1.4a, HDMI 2.1
Execution units
32
Max. Resolution (HDMI)‡
4096 x 2160 @ 60Hz
Max. Resolution (DP)‡
7680 x 4320 @ 60Hz
Max. Resolution (eDP - integrated flat panel)‡
5120 x 3200 @ 120Hz
DirectX* support
12
OpenGL* support
4.5
OpenCL* Support
3.0
Multi-Format Codec Engines
2
Intel® Quick Sync Video
Yes
Intel® Clear Video HD Technology
Yes
Number of supported screens ‡
4
Device identifier
0x4680

Intel graphics controllers (4th generation and newer) support 4K resolutions (4096 x 2160 or 3840 x 2160) with refresh rates up to 60 Hz.
The video output on the computer and the video input on the display is either DisplayPort* 1.2 or HDMI 2.0. For HDMI 2.0 and 4K@60hz, the cable must be classified as high-speed HDMI.

Note: Memory type DDR4 RAM 3200 MHz SO-DIMM
None DDR5 RAM 4800 MHz SO-DIMM important for video and larger image processing.

Sorry, I don't know the answer