Probably just some random announcement like they usually do with hardware revisions.

Probably early next year. Nintendo's console cycle periods usually run for 5 years (the GC and Wii life cycle were 5 years and Wii U was 4 years) so I'm expecting their next console to be the switch successor, not an upgrade version of the switch.

either just before the holidays... or early 2022.

If we take the Switch Lite route, next month

If we don't, when the Switch will start to fall from that infamous cliff

Exactly same thought, with Zelda BotW 2 along with it on March. 

If we still have problem with the Switch demand/production, I don't know then haha, they are going to start thinking about Switch 2 probably.

When they're getting ready to release Breath of the Wild 2.

Wii life cycle was 6 years.

OP: Switch XL should be announced early 2022 with a release within this fiscal year, probably March 2022. A proper Switch successor should follow 2025. If no Switch XL will be released, a Switch successor should launch 2024.

There's still a chance that a Switch XL will be released this year. Switch Lite was announced 10th July and released 20th September. Imo there's no real need for new Nintendo hardware this year. Nintendo, Sony and Microsoft still struggle to satisfy the demand of hardware and Nintendo is still selling out all competitors combined.

The Switch is on it's way to increase sales over 2020 in 2021 with keeping up with the momentum of last year and having a much beefier late year season than last year. Usually the next gen is started at least 2 years after the peak of the previous gen hardware. Nobody ever has brought the next gen amidst the peak of the last hardware.

As Switch seems to be able to peak this year without a Pro, I think early next year might be a good time to push new sales and start the second half of Switch's lifecycle.

If it ever exists, I agree with after the holidays, early next year. Sidenote, I just knew nothing would be announced before at at this E3, I just knew it.