Hi michael
"... . I DO have some experience. I like your word SHOULD. Pls try it for yourself. We talk about facts here, not "should" and "could". I have spent some hour on this, enough for now. ....."
As an author I am sure you have more than some experience.🙂 However, I use of the word "should" in the conditional sense .....i.e. provided everything else is correct...Unless something is wrong the project should** export OK. with the stated 320 kbps audio quality. etc. I do not mean to say that it will.
" The .avi is just a container for the MP4" - it seems, that you do NOT know about this subject. "
I am sure you are correct. in this 🙂. I can only go by the fact that the VP export window allows one to select .avi and choose the MPEG4 (Native) codec and the exported file is an .avi. The contents I assume are in mpeg4 compression....please correct me if I am wrong .....and then explain why VP says MPEG4 (Native)....As far as I know AVI files may use different types of compressions (MPEG4, DivX, XviD, RM, etc.) to encode the video. I hope you can see where my statement is coming from.
"@Nationalsolo: your screenshots are NOT correct. they show video encode being MP4, but actually you are displaying audio after selecting .avi video format "
In the example I illustrated you are correct...I selected .avi. before selecting the video compressor (MPEG4 (Native)
Nevertheless as I stated and illustrated above VP will allow you to export an MPEG4 (mp4) with 320 kbps audio quality. Which is apparently what you want and say you are not getting.
Instead of then selecting .avi, (which you don't want,) you select mp4 from the drop down list. This allows you to choose MPEG4, H264, or H265.
So, select MPEG4. and as stated above, 320 kbps is available from the Audio Quality list.
See the MPEG4 export settings below...... This not an mp4 associated with the .avi container which is MPEG4 (native). It exports as an .mp4 at 320 kbps

Are you saying this is incorrect or not working for you or you are not seeing 320 kbps?
Regards
Nat