When Nintendo launches their new console how long do you think they will support Switch by releasing new games and manufacturing the console?

I'm thinking 2 years.

I find it hard to believe that Nintendo will provide much additional support for the Switch following 2024, especially knowing their track record. Times have changed, however, so I could very easily be wrong on this.

Consoles production will continue through 2027, if I were to guess.

At least a year after the successor's release.

2024: Exclusive games (number of first party releases on par with 2023) - selling 10-15 million
2025-2026: Cross gen games (Metroid Prime 4, next 3D Mario, Mario Kart etc.) - selling legacy numbers, 7-8 million a year
2027-2028 - Winding down production, the last 5 million

Nintendo will release some minor games in 2025 but basically nothing after that. I can't see Nintendo going the cross-gen route and releasing most titles on both systems in 2026 and later. I expect Switch hardware shipments will end by March 31st 2027.

Unlike the 3DS there is not really going to be a space on the market for the original Switch once the Switch 2 comes out. The 3DS had it's own library of games that were not playable on the Switch while all Switch games should work on Switch 2. I'm also not expecting them to cut the price of the Switch and rather focus on getting people to adopt the new console.

It's dependent on when Switch 2 launches.
The most likely quarters for Switch 2 to launch (in this order)
1. Q4 2024
2. Q1 2025
3. Q3 2024
First-party software will continue through 2025, maybe even 2026. Hardware won't be discontinued until 2027 or 2028. eShop will probably be open a long time still since Nintendo might build Switch 2's eShop off of Switch's eShop.

I believe the Nintendo Swith will be supported for another five years.

The Switch Eshop is such a mess because of the lack of legitimate software verification that we end up with a shit ton of shovelware, worst than the Wii days. So I'd prefer to see them to clean up the act on their 2nd go around and starting a new. If you want to download titles that we're previously on the Switch Eshop. You just go back to it and download it there first.

Nintendo has already stated how long they will support the Nintendo Switch for.
President Shuntaro Furuwaka stated that we are "still working on software for the Switch for the fiscal year ending March 31, 2025"
March 31, 2025 will be the last day any Nintendo published games will be released on the Switch.

Nintendo Online Support, online multiplayer support, eShop support, and Hardware manufacturing are a different thing.
I think that the successor will have all of these but specifically declare the Switch support for these will be discontinued respectively in April 1, 2030; April 1 2030; April 1, 2029 & April 1, 2027.
3DS eShop closed 12 years after its release and online services close 13 years after its release.
Furuwaka stated that the Switch was at its halfway point in its lifecycle by its 5th year, which is 10 years of shelf life. 

1 year after the SwitchU releases.