250Hz is the native polling rate of PS4, Xbox One, PS5 and Xbox Series X over USB. Sync interpolates XIM APEX's output polling to 30,60 or 120Hz to sync the device with a game's processing loop at that frame-rate. That can result in very stick aim assist, but in some games like CoD, the aim assist bubble can be harder to pop. In those cases, bumping Response Rate to 500 or 1000Hz with Sync Off can help.
XIM APEX RR at 250Hz with Sync Off ensures that XIM APEX is polling at 250Hz to the console, which is what the console is expecting input to be over USB. That should provide more controller-like game behaviour for things like AA by using native console polling rates...at least that's always been my hypothesis.
Ultimately, it comes down to preference and few people have ever really tried 250Hz. I used 250Hz for the entire alpha-testing phase of APEX because Titan Two (also alpha-testing at the time) didn't support XIM APEX at 500 or 1000Hz. XIM4 at 125Hz to XIM APEX at 250Hz was a revelation, but I didn't find 500 or 1000Hz to be of any more benefit, while introducing things like jitter into the mix.
i agree with all of your findings except for the off sync has more aim assist that for my setup is not even close its alot less BUT to counter it i added 35 Simulate analog behaviour now i have super snappy feeling with good aim assist 
have you tried any SAB that will change all your findings again but id be curious if its changed anything for you if you did
I experimented with a script on Titan Two prior to SAB that interpolated keyboard input to take advantage of left-stick AA. Digital (kb) input ignores l-stick AA by ramping straight from 0 to 100%. But adding acceleration from 0 to 100% over say 200ms proved to be effective for l-stick AA, especially in CoD and similar games. The same effect on l-stick AA is true of SAB on XIM APEX because it uses a similar (but more complex) method to obfuscate digital input. Neither method is as good as true analog stick input for l-stick AA because you can't hold a value of less than 100% using digital input (my script also had an editable max speed cap to counter this).
Long story short -
1. for right-stick Aim Assist, I highly recommend setting mouse polling of 1000Hz, XIM APEX RR at 250Hz and Sync Off as a starting point.
2. for games with left-stick AA, definitely add SAB into the mix (I'd go with 35 or so too).
That said, I tend to stick to 500Hz and Sync Default as I can't be bothered endlessly optimising XIM APEX expert settings. I'm just not that invested in any one game and these settings feel ok for everything. I also use analog input via Azeron for true analog behaviour, so I have no need for SAB.
