The earliest I can see a Switch successor coming is Holiday 2024, but I can also see it being pushed to 2025.
Since there's no competition for Nintendo to worry about like with the PSP or Vita, which is why the DS came out in 2004 and effectively cut the GBA's life short, or why the 3DS came out in 2011 even thought the DS was coming off a 20 million year and still had plenty of juice left.
This time around, since there's no real, direct competition in the handheld (or hybrid) market, they can take their time and squeeze every last drop they can out of the Switch before they formally move on to the next system.
Hardware Comparison Threads:
Current Thread
Is Hardware Getting TOO Powerful?
Older Threads:
PlayStation/Xbox/Switch: 2022 Edition
PlayStation/Xbox/Switch Hardware Battle: 2021 Edition!
PlayStation 4/Xbox One/Nintendo Switch: 2019 vs. 2020
PlayStation 4/Xbox One/Nintendo Switch: 2018 vs. 2019
PlayStation 4/Xbox One/Nintendo Switch: 2017 vs. 2018
PlayStation 4: 2015 vs. 2016 vs. 2017