Did you manage to make it rigid? Have you tried to "bend"/move assembly towards spinning work piece? Do you use whatsapp, discord?
Ok so Im not a machinist im a automotive repair tech so I just look at a lathe as a piece if equipment and just treat it like a part on a car.
So this may not be correct but
Your lathe will have a certain amount back lash or movement in the assemblies.
So when cutting you apply the cutting tool to the work, you now have forces pushing against the tool holder, the saddle, the cross slide the compound so there’s always going to be a little backlash or free travel if you force that back in the opposite direction or towards the work. You also have to remember to use your carriage lock your compound lock, your cross side lock when you’re making cuts as this will help eliminate any movement but you have to be careful because you don’t wanna crank those locks so tight you’re now moving the assembly or bending the Gibbs if the lock is pressing against the Gibbs I’m not sure if that makes sense without actually showing you in the video which I am not good at
Although my lathe was used, it was not used enough to actually be worn and when I had a friends dad who was a master machinist come look at it. He just laughed and said it was never cleaned properly from day one because it still had Cosmoline all over it and it was never properly adjusted oiled or gone through, in the end, I ended up stripping the entire assembly down cleaning everything taking a fine diamond stone hitting all the machine surfaces just enough to break any high spots or nicks or burrs cleaned. Everything got all the Cosmoline out of it. I was shocked at how much crud came out of the Ways surface , there was so much crud buildup that you cannot really see the scrapings. Now once I got it all cleaned back together, well oiled and adjusted. Everything moved and slid nicely and then took about three or four attempts to get all the play out of the saddle, the cross slide , in the compound, I just kept going back and forth making very small changes are eventually I came to a point where I need a dial indicator to test to see if there’s any movement. Now my best indicator is only three digits to the right and I have everything set up , you can barely see anything move on that needle which I feel is well within this machine’s capabilities.
I think the big problem is the manufactures of these Lathes Assume you’re a machinist and know what you’re doing so the instructions are off, awful vague, and sometimes just nondescript. In the end, it took scanning through many videos and reading a lot of how to run to lead articles online, although it’s funny, there are plenty of books on how to run a lathe. The one I was thumbing through didn’t have much in the way of how to set up your lane is keep at it you’ll get there.