It's a .kip file, and apparently you'll have to find it somewhere online, they stopped hosting it on the official repo because for general use it's not recommended to use it.
I actually found a copy in an old commit on tumGER's SDFiles repo:
https://github.com/tumGER/SDFilesSw...7a2c9978d4dc896/Hekate/modules/nx-dreport.kip
You have to set it up to run as a module, in Hekate you'd add it to an entry in your hekate_ipl.ini file. Or with ReiNX you just drop it in a /ReiNX/sysmodules/ directory.
Yes, you can switch between CFW and Stock, but it's always a pain in the butt to do. It will be much better when we get true emunand. For now, any time you switch to stock you have to restore your latest "clean" nand backup, and then any time you want to start using CFW you need to make a new "clean" NAND backup first. If this sounds long and time-consuming, that's because it is. Emunand will make this much easier. Another alternative is to buy a replacement eMMC board for your Switch off of eBay or aliexpress (they run around $20). Then you can flash your NAND backup to the replacement board, and switch back and forth between them. Perhaps you can cut a door in your Switch casing to make this easier.
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I just realized you said you used ChoiDujour to update to 5.1. 5.1 added flags that will get you banned for clearing error logs. I personally still run nx-dreport at every boot and haven't been banned, I personally think it's more likely to receive a ban for an error log being saved and sent out due to homebrew use than a slight inconsistency with the number of error logs, plus since I run it every time I get an error no errors really get an opportunity to be sent out.
Do with that what you will. You don't have a "clean" NAND backup, there's no way of 100% guaranteeing that you're not going to get banned sooner or later. Might as well take a few obvious precautions (like not using backups online), and enjoy playing online while you can.