Are there credible technical bases for reports of “Apple deliberately slows down older devices when new software is released”?

Apple uniquely controls and shapes the experience of iOS. If you do not trust Apple, do not buy an iPhone.

Considering the impact of Apple's past behaviour, Apple settles iPhone slowdown case for up to 500M USD and a 25M EUR fine by France's DGCCRF for slowing down old iPhones, it would seem foolish to attempt the same approach twice. It appears Apple will now inform you before slowing down your device.

It's true that Apple added code to iOS update 10.2.1 in January 2017 so that if your battery had degraded sufficiently, it would run slower, to avoid sudden shut-offs if the power rose too high for the battery to cope.

But that's a world away from deliberately making all older phones run slower with the express intention of making you upgrade, and there is no evidence to suggest that.

I have an original iPhone SE (c. 2016-2017). I had the battery replaced in 2019, because it was shutting down and showing erratic % reporting (on iOS 12). Since then, it runs very well on the latest version of iOS (14.6), with no signs of any slow-down.

Also, I would suggest that 'people searching Google for the term iphone slow' and 'people having problems with slow iphone' are not the same thing.

OS updates download onto the phone in the background, and may use up all the remaining space, if there's not much left, and this by itself would cause sluggishness, before the update was installed.