I buy blades in 26 and 32mm depths for 2 and 3mm inserts. I didn’t get on with the GTN style at all and use Kyocera, Kennametal and the double ended MGMN which are currently favourites. Insert blades have an advantage over one piece holders as they are double ended giving two lifes.
The size of lathe makes a huge difference and if possible part off under power. Rear inverted toolposts can help and a dedicated parting off toolpost fixed directly to the cross slide eliminates some of the flexibility of the top slide. Also locking of the carriage adds to the stiffness.
At home, my 7 x 12 mini lathe works well with a holder with a tapered 2mm HSS parting off blade in a little holder.
This is a regular subject on more than one forum.