In general with any specialized equipment, you need to pinpoint a key area of improvement in the main lift and then decide if the specialized equipment (in this case, the Slingshot) addresses this. Some things I would, and have used a Slingshot for…
-Adding in more weekly bench volume without overworking the shoulders. You’re most likely to get “beat up” from benching due to heavy loading when the bar is at your chest. Lots of tension on the pecs and shoulders, and they’re not in a very strong position to begin with. If benching 2-3 days a week leaves you with aches and pains, throw the Slingshot on for one of the days. The reduced loading at the bottom of the movement while still getting some lifting in might actually help with blood flow and week to week recovery.
-Dynamic effort method work is much easier to do with the Slingshot, as opposed to chains and bands. Without getting too far down the Conjugate rabbit hole, the DE method is centered on moving submaximal weights with maximal speed, which leads to maximal force production from the muscles. Accommodating resistance (bands, chains, slingshot, etc…) is ideal for this since it allows the load to be heaviest at the (generally) strongest point of the lift (lockout) and lightest at the weakest point (chest), so when pressing the weight as fast as you can you have a nice, constant bar speed rather than a continually accelerating speed. So for DE method work, a Slingshot is basically just a convenience over chains or bands.
-As you mentioned, overload work is a great use for the Slingshot. Overload, in practice is putting over 100% of your 1RM on the bar and either statically holding the weight at the top, or moving it through some reduced range of motion. It’s a great tool for notice and intermediate lifters, and definitely has a place with advanced lifters. The primary benefit of overload is forcing the lifter to develop full body tension (maximal muscle recruitment) in the lift. If your max bench is 300 lbs, and I put 400 lbs on the bar and have you unrack and hold it for 10 seconds (with safeties, of course) you will, without realizing it, contract far more muscle throughout your whole body during those 10 seconds than if you were holding 300 lbs for 10 seconds. Now, if you practice that regularly and learn what that whole body tension feels like, then you can start creating the same tension during the rest of your benching. More muscle recruitment = stronger bench. The Slingshot accomplishes this by supporting your body in the weakest part of the lift, allowing you to “feel” weights above your 1RM.
-Similar to overload, the slingshot is useful for triceps targeting (strength and/or hypertrophy) since it assists the least during the lockout, where the triceps are doing the most work.
As with any assistance/accessory exercise, if you don’t have a very specific “why” for it’s existence in your program, then you’re basically rolling the dice on if it will actually lead to progress. Always start by finding the weak points in the competition lifts, then find the appropriate accessory movements to address these weak points. Programming doesn’t have to be super complex, but it should always be very intentional.