If it has good speaker in it, in the worst case you can just cut/throw away all the "smart" electronics out of it and place something like a RPi + an amplifier inside to have a mini media center.
zerowaste
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I've done something similar - repurposing old 90's boomboxes with hifiberry - it works relatively well (but does require some tinkering.
How difficult would this be to do?
Depends on which setup you'd like to go for.
Disassembly aside (no idea how Alexa looks like on the inside), you could go for something simplest: take a RPi 1B/2/3/4, plug in the 3.5mm jack into it and solder the other side directly to the speaker. This, in theory, should work out of the box and give you some decent sound (and probably even okayish volume).
If you want to go more elaborate, you might use some smaller/cheaper computer (e.g. RPi Zero 2W) + some tiny external DAC+amplifier. In this case you will have to ensure that the DAC is compatible with your computer, that the software is there and also handle power supply to both of them, and possibly also take care of the 50/60 Hz hum induced by it (depends on the power supply, the DAC and its wiring).
You could go even cheaper with something like this: https://arduinoyard.com/dfplayer-mini-with-esp32/
But here you start hitting a limitation that it won't be a regular Linux machine anymore, but a microcontroller with its own set of capabilities and interfaces that you'd need to handle.
For example, in this configuration it would be able to play MP3 files from an SD card, but probably not the web streams (even direct ones) or something of that nature — for that you'd need a different setup, I guess.
It was e-waste the moment it was made, its not your fault.
I don’t have it in front of me but it’s the cylindrical fabric speaker that looks like this:
That will be nice if I can put Lineage OS on it. Though I have to wonder how useful a headless unit could be.. if I could get a remote display on my PC that would be cool.

Repurpose the battery? Short of scraping it for parts, I'm not sure Amazon designed it to be anything other than their spying tool
You could replace the microcontroller with an ESP32S3 and use the speaker and microphone with Home Assistant/Music Assistant or Willow voice assistant to essentially replace a lot of the real-use functionality: lights, music, and timers that Amazon said itself was almost all of its use according to their data harvesting 😂.
It depends how DIY/electronics savvy you are or if you are looking for a project.
Not sure if you want to do that, but:
Exchange leds, mics and board and build your own localized or cloud based (for example homeassistant) voice assistant.
Or send it to me ;)
I am currently in the process of de-Alexafying myself, and I had the same question. Unfortunately I haven't found any real answers.
somehow amazon has managed to make fire products that no one seems to be able to jailbreak or such. I mean there is tons out there so its not like its not a good target.
Last I checked people were into both their tablets and tv sticks. "Jailbreak" an alexa and you end up with a shitty wireless speaker, not a lot of incentive there
New fire tablets are ostensibly impossible to remove the OS from