Enable Graphic Rendering CUDA when exporting

It's not the graphics driver at all, according to the screenshots that I looked at. You are already running Premiere Pro's renderer in CUDA mode to begin with. If you are running a version of Premiere Pro prior to version 14.2, you are locked to software-only H.264/HEVC encoding because your CPU has no QuickSync encoder or decoder at all whatsoever. (All F- and KF-series Intel CPUs have their integrated Intel UHD Graphics permanently disabled during manufacture, and thus QuickSync is also permanently disabled on those CPUs as well.) Those older versions of Premiere Pro support only Intel QuickSync for hardware encoding (QuickSync hardware decoding and encoding REQUIRE that the integrated Intel graphics be both present and enabled). Beginning with version 14.2, Premiere Pro now supports NVENC and VCE/VCN for hardware encoding. Hardware rendering is completely different from hardware encoding, in this case.

So, to utilize hardware encoding via your discrete GPU, then please update Premiere Pro to version 14.2 or later.