You won't, I have a digital copy that I've also installed and played from my profile on my boyfriend's Switch. The game is tied to your profile, so as long as you connect the profile on your new Switch to the same Nintendo account, you'll be fine.If I were to get a switch lite, would I need to buy another copy of animal crossing? I own a digital copy on my husband's switch.
The only problem is that you can only have one console designated as your main console, and you're somewhat limited on the secondary console - other profiles can't open games you bought digital copies of, and you need an active internet connection to open games from your profile. It's not a big deal if you have a stable internet connection, though - my personal Switch is actually my secondary console, since my boyfriend had bought games on my profile, and I barely, if ever, have had issues with it.