Early 2025

No way that we'll see another holiday season without new hardware. We don't have any numbers for December '23 yet, but November was 40 % down year-on-year. Switch should sell below 10 million units in 2024 (which is lower than the first full year 2018) and unlike during the Wii U / 3DS era Nintendo has no other device to sell.

Nintendo announced Switch in October 2016, because they knew that Wii U wouldn't sell that many units anyway. An announcement in January and release in early March wouldn't have been enough time and they would have angered customers as well who would have bought a Wii U in December. Nintendo needed to release Switch in March to improve their fiscal year results.

As for Switch's successor, I expect that Nintendo mentions new hardware in May during their fiscal year report, a full presentation with name and launch titles in June and a release in November 2024.

I come from the future: The Switch 2 will be called the Nintendo Dual. It releases on

Probably around the time where E3 was held in the past

Looks like rumors are turning a bit more into concrete evidence.
Niko Partners, a big China market intelligence, has great ties in the gaming world including: Activsion Blizzard, Google, Nvidia, Sony, Take Two Interactive, Tencent, Unity, and Nintendo.

https://www.vgchartz.com/article/459507/analyst-predicts-switch-successor-to-be-announced-in-2024-ps5-pro-to-release-this-year/

Based on this if Nintendo announces the NG this year, then it should be releasing in 2025.
I want to predict March 2025, that way they can have the immediate die-hard fans, and the 2025Holiday season build up for games.