Glad to see it's working!
I didn't see this thread initially, and you moved away from carbide inserts so this is only directed at the initial problem and setup. I say that since it's a good bet at some point you will want/need to use carbide insert tools.
The carbide insert tool you were using is definitely a turning tool but it's not really meant for facing. It would have worked for turning but the orientation of your compound/tool post was wrong. That tool shape is for when you aren't going to be turning to a square shoulder and/or want to leave an angled shoulder. It can also be used to make chamfers as mentioned.
I said the compound/tool post was wrong, so we need to take a bit of a step back. One of the benefits of carbide insert tools is that they take some of the guesswork out of setup, but there's a gotcha in there you have to know from the start. Carbide tool holders in a QCTP assume that the tool post (really tool holder) is going to be square to the face of the chuck. They have the angles built in to the holder so all you have to do is square up the tool post to the face of the chuck and you're set other than making sure the insert tip is on center.
In addition to using carbide inserted tools, parting requires the tool to be absolutely square to the face of the chuck (or absolutely perpendicular to the work if you want to look at it that way) so it's a pretty important concept.
There are two easy methods that normally work on any lathe. One, is to slightly loosen the tool post so it can rotate and push the side against the chuck jaws (works best if the jaws are in good shape). To eliminate the jaws as a variable I like to use a 123 block on the face of the chuck and then move the carriage until the tool/tool post push on the 123 block...that will get the tool perfectly square, then tighten the nut on the tool post. I actually like to use the tool itself on the 123 block to eliminate variation in the tool holder and tool post. If the tool itself is square to the chuck, that's all that really matters.
I picked up a couple of scruffy 123 blocks super cheap at an estate sale a while back...cleaned them up and they're good enough for stuff like this:
The later posts with the HSS you had ground for you show how it's easy to get confused about which angle goes where when you're new to this. With HSS you often have to move the tool post around and combine that with grinding angles, relief angles, etc into the tool so there are a lot of variables involved. I won't argue that being able to grind HSS to a useable shape is a bad skill to have, but for a lot of things I like just being able to drop a tool in the holder and get to work without fiddling around with the tool post orientation, etc.
Here's a pic that shows how inserted tools (this is a CCMT insert holder) have the angles built in from the start using a piece of scrap for reference. This tool will face and turn to a square shoulder and all you have to do is get the tool square to the chuck and on center.