First BIG question ... where are you getting troubles with "software encoding"?
As ... if that is in the summary for an export process, this has nothing to do with your GPU whatever.
This gets confusing as the same phrase is used for two completely different things.
- The 'expected' one is Premiere using the GPU for normal GPU stuff, like Warp, color, resizing, some other effects.
- The OTHER way this is used is ONLY when you are doing an H.264/5 export. It has to do only with the long-GOP capabilities of your computer, which are NOT GPU related, and at times whether you have the options for H.264/5 encoding and decoding "if available" checked ON in your preferences.
Further, NO 2-pass H.264/5 encoding is 'hardware supported' on any system anywhere, that's not an option at all. 2-pass means the CPU analyzes the sequence frame-by-frame in the first pass, then encodes on the second pass.
No hardware H.264/5 chip can do that process.