Data point: arrived SGN from SAI flying VN business. Time of arrival was about 8:30 pm on a Tuesday. There was zero line at immigration. We had Fast Track due to VN Business, and I didn't see a separate queue for Fast Track but didn't bother looking very much as there was no line at all.

Data point: departed SGN for DAD flying VN premium economy. Was able to check in at Sky Priority which had no line. Security was pretty quick too - about 10 min. This was on a Sunday at about 9 am.

Note that VN flies out of T3 for domestic flights at SGN. I messed up and had our Grab driver deliver us to T1 as that is also a domestic terminal, not realizing there is another one. We had to wait about 15 min for the free shuttle that runs between terminals. It only runs every 30 min and the transfer from T1 to T3 takes some time so if you mess up like I did it could result in a substantial delay for you in terms of making your flight.