Parting-tool tips are also made with a cutting-edge that should be parallel with the lathe axis with proper machine-setting…
Please note that the ones in the original post are denoted N151.2.
If you look at Sandvik’s literature on the Q-cut system, you find inserts with L151.2 and R151.2 designations.
These do not have a parallel (the N is for neutral) cutting edge and are made specifically to leave the ‘pip’ on either the part being cut off or the part remaining in the spindle. As with the neutral ones, they also curl the chip so it is thinner than the kerf of the tool.
Sophisticated manufacturers offer options.
Your comment about side loading needs deeper consideration. Every insert parting blade you buy will be deeper, and hence stiffer (even in the side direction) than an HSS blade cutting the same kerf. Perhaps you could watch this video on YouTube (https://www.youtube.com/watch?v=c4w-ulo3l3g entitled Tools In Action: GARANT grooving) and write to Mr Hoffman to advise of his mistake.
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On the thickness issue, 2mm seems to be the minimum that is generally described as ‘parting’. Below that, the tools are known at ‘grooving’ and sometimes ‘parting/grooving’. It is a change in nomenclature.
An economic semi-universal insert of that type is the MGMN insert, which also comes in a semi-circular form fitting the same holder as MRMN (so MGMN300 is 3mm wide and MRMN is 3mm dia semi-circle). The round-ended ones can be used as a smaller diameter continuation of RCMT inserts, which stop at 5mm dia.