There is already a widespread notion of "general computing" device.
For all intents and purposes, a laptop computer and a smart phone are one. This is, for example, evidenced by the fact we run general purpose "applications" on them (not defined ahead of time), including a most general app of them all (a web browser).
For other device types you bring up, I would go with a very similar distinction: when you can run an open ended app platform like a browser, why not be able to install non-browser based applications as well? Why require going through a vendor to do that?
"why not" isn't a compelling case for something to be a fundamental right.
I'm not saying I dislike the concept of being able to run my own code on my devices. I love it. I do it on several devices, some of which involve circumventing manufacturer restrictions or controls.
I just don't think that because manufacturers started using the same chips in phones as computers, they magically had new requirements applied to them. Phones had app stores before they were built using the same chips. My watch lets me install apps from an app store.
You've asked for an intrinsic difference between a class of devices: no, you are unlikely to want to run general purpose apps on your washing machine. Yes, you are likely to do so on your smart phone. Probable on your modern "smart TV". Low probability on your eReader.
Legislation like EU Cybersecurity Act hopefully pushes things into more of a fundamental rights thing by demanding that devices don't go into the trash pile as soon as the vendor stops issuing security updates by mandating an ability to keep operating these devices without negatively affecting Internet at large (by, for example, becoming a part of a botnet).
This is already possible with many general compute devices by putting a version of up-to-date GNU/Linux or FreeBSD or... on it. And for a smaller subset of GC smartphones, with AOSP-based Android.
I'm not asking for an intrinsic difference: I'm suggesting that if "I can install custom applications/code on this device I own" is a fundamental right, there would need to be an intrinsic difference. My personal opinion is that there is not an intrinsic difference. That "I want to do it to these devices and not those" can't be the justification for it being a right that I'm able to.
To counter your claim, I've tried to explain what that intrinsic difference is in my previous comment.
I am not sure if you are disagreeing with me or ignoring my point :)