I feel ya. Shoulder impingements are not something that can always be returned to utmost functioning. I know I warned you about that but I certainly hope you'll be able to get back to benching. I know that's tough. I'm pretty sure you'll be able to get back to squatting but in the meantime you are getting much stronger and it will only aid the squat in the long run.
When you do try to bench try it with light dumbells. That way you can keep the elbows tucked in tight and do it in a natural way that is most comfortable. You're going to have to learn to love the dumbells for now. The straight bar in general is much tougher on the shoulders.
On the laterals with the shrugh work on increasing the range of motion if you can. Even if it's just a tiny little bit. There is actually a version of overhead shrugs that are like laterals starting with the arms at a parallel to the the floor position. So that you raise the dumbells up sideways to a point overhead that is similar to the grip you would use for overhead barbell shrugs. Which is to say a kinda wide grip. Then you shrug up. So that's a different alternative to regular overhead shrugs but of course the weights would be much lighter.
In your case what you could do is try that exercise with very light dumbells and the arms starting paralles but only raising it as much as you can and then shrugging. And then work on increasing the height of the dumbells before your shrug. You could also combine that concept with the regular laterals sometimes where you start with arms at the side but then go up higher than you normall would for lateral. Except for that I would want you to use a good bit lighter weight than for the plain lateral (in scapular plane of course).
Hope some of that makes sense
If the shoulders are being that stubborn it would be great if you could hook up with a pysiotherapist who knows about lifing. I know that may not be possible. If so though the questions would be what else can you do to ensure that scapular mobility is up to par? How do you assess that and know when it is time to start specific strenghening of the external rotators? Since I am not right there with you it's hard for me to know what is going on.