Same cassette on the trainer all the time for me. I have a chain wear indicator in reach, and check it once a month, or every time I lube the chain (whichever comes first). If you keep chains with minimal wear on both bikes, you should not have too much problem with the cassette.
That said it can depend on the specific cog or range of cogs you use. If you lock into a single cog for ERG, that one will see more wear and may lead to the need to replace the cassette at different frequency from the chain.
Your chain isn’t wasted, you have used it plenty it seems. Chains are wear items. Of course, you should keep them lubed properly to maximize the life of your cassette, chainrings and chain.
Regarding cassettes, if you are using a smart trainer on erg mode, I don’t think your choice of cassette matters much. I’d just take similarly sized cassettes to make sure the alignment isn’t off. (If you have, say, an 11-32 cassette on your wheels and an 11-23 cassette on your trainer, the size difference between the largest sprockets would be quite sizable and could lead to problems when shifting.)
If you are using your trainer in dumb mode or you had a dumb trainer, then you can go either way: you could choose a cassette with smaller steps between the gears. This allows you to fine tune your cadence. Or you could insist to use the same cassette as outdoors, because you will be forced to deal with the same gaps between the gears outdoors.
I’ve taken to waxing my chain because it keeps the rest of the drivetrain clean, but I think it’s really useful indoors. Since the chain isn’t exposed to the elements, once the drivetrain and chain are clean and the chain is waxed, the whole system stays clean. The wax lasts until it wears down. I’d guess 30-40 hours for me.
I have one bike with an 11-28 cassette and one with an 11-32, and I leave an 11-28 cassette on the trainer so that it works fine with either bike.