Hi Ali,
Yeah, there's something screwy going on if the rear cover doesn't fit any longer. If everything is done correctly, it should sit down exactly on the frame all the way around. Given that the rear cover is glass, that means it's not a matter of having been deformed when you removed it; glass just isn't that flexible. So you're going to have to go over your work again and figure out where the problem is.
I'm looking at the battery replacement guide and there are three parts that get removed; the battery itself, of course, the wireless charging coil, and the lower speaker. Most likely one of those things isn't sitting inside the phone quite right and is keeping the cover from seating correctly.
So yeah, go order yourself a couple more sheets of precut adhesive and resign yourself to opening it back up. Remove the adhesive first so you'll be able to do test fits without it sticking down, then start disassembling again. I'd try taking off the wireless charging coil then see if the cover fits. Put it back on, then take off the lower speaker and try again. Pull the battery then refit everything except the battery and do a test fit. Somewhere along the line you'll see which of those parts is getting in the way, and once you do you'll have to figure out what to do about it; usually it's a matter of making sure the part fits in where it's supposed to go. I'd double-check the replacement battery against the original to make sure it isn't thicker, which would cause the kind of problems you're seeing.
By the way, when putting the rear seal on it usually goes onto the phone chassis rather than the rear cover. There's no specific guide for putting that on, but here's a general guide that should work fine.
How to Replace the Back Cover Adhesive (Frame First) - iFixit Repair Guide
Good luck; let us know what you find!
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Did you remove the old adhesive from the glass and the chassis of the phone? Try and find genuine Samsung adhesive. Aftermarket stuff is absolutely garbage.
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