The specs for the car call for 255 40 19 tires on 8.5" rims. That is what I have now. I am swapping the rims for Jaguar Caravelas which unfortunately are staggered, 8.5 & 9.5

If I put wider tires on the rear there is no exact match for what I have now, 275 40 is .6" greater in diameter/18 revs fewer or 275 35 is .5" smaller/ 14 revs more.

Will this make any difference on anything? I am familiar with the consequences of doing this on an AWD drivetrain, but not on this, RWD.

As long as the ABS self check doesn't see the difference in RPM as a system fault, I think you'll be OK. No idea what sort of tolerance it has.

What if I put the same size tires on the staggered rim widths? I have searched on line and obtained inconclusive data, some saying it would work and some saying it would not work and still impact overall tire diameter.

When I swapped from 20 to 18 I had the car reprogrammed with the new size wheels, but you are fitting two different widths rather than diameters so I'm not sure if this is possible to program.