Use it as my gaming rig

sent from my i5-750 with 8 GB RAM

Only somewhat kidding. I don't use that machine to browse the internet as it uses too much electricity for idling 90% of the time, but I do actively use it for games that require a "beefier" GPU than the iGPU of my laptop (which usually just means needing more VRAM. Damn modern games).

Pre-post edit: Sorry for the long text, this definitely got out of hand and might not even be very useful 😅

[...] use it for experiments [...] Turn it into a local server, NAS, self-hosting box

I'd be curious what kind of experiments require additional PCs. Networking stuff and self-hosting comes to mind, but that doesn't necessarily require additional PCs, and desktop-PCs tend to have too high power consumption for letting it idle >90% of the time. NAS servers or even something like jellyfin also don't need a lot of compute power. My jellyfin server is running on a 15 year old shitty but very trusty 18 Watt E-350 APU. Then again, don't listen to my negativity - if you have a use case for that PC, use it!

Use it to learn more about local AI, although I assume the GT 730 is far too limited for most modern models

I'm not familiar with local AI, but I wouldn't expect to get far with that GPU if you mean LLMs. Maybe if you have the 2 GB version, but even then, it will be slow. It has, even for its time, very slow memory and seems like it was never designed for any intensive workloads. That GPU only has compute capability 2.1, no Vulkan support and only OpenCL 1.1. That's good enough to start getting into GPGPU programming if you wanna play around, but LLMs sound like a stretch, not just performance-wise, but also software-support wise. But I have never tried running local LLMs myself, so maybe software-support isn't that much of a problem.

Also, and this is definitely just opinion from my side, but I would say running AI, even locally, might be somewhat against the idea of permacomputing glancing at the side bar

Sell it cheaply and put the money towards a newer, more energy-efficient machine

Thing about this is, that if you sell it so that you yourself will get a more energy-efficient machine, that PC will still be out there being used by someone else, so not much gained efficiency-wise. However, and I am contemplating writing a post about this topic here at some point, the production of a PC is responsible for the majority of the energy required in a PCs whole life-cycle. Selling (or trashing) this PC to get a more energy-efficient one might not save energy overall at all, at most it would reduce your power bill, but even then the question is whether it would be worth it compared to what a new PC costs (electricity really is cheap, you really have to run it 24/7 to be worth it). Efficiency is kind of a scam when it comes to reducing overall power consumption, but that's a topic for me rambling another time. You have to use a computer very long to make up for the energy required for its production with the efficiency gains.

What I want to say: if you want to do the environmentally friendly thing, use this PC as long as you can, instead of replacing it with a newer one (assuming you have a use-case for it).

What would you do in my situation?

If you already have a new PC (which I somewhat expect), then... errr... I don't know. I have a similar problem - just last week I have been cleaning three PCs that a friend of mine wanted to throw away. I'm even considering using one of those as my new gaming PC, but I'm not sure yet if I can separate from my PC after all those years. I'm probably just going to fix them up and bring them into good shape for the next LAN party, but otherwise I also have no real use for them. Kind of sucks letting all that hardware go to waste, I can't use four PCs at the same time, and other people usually want the latest hardware.

For real though, probably a mixture of salvaging parts and still keeping the remains, if it's a PC that is not in active use. SSDs and HDDs are the easiest to reuse, and SSDs also tend to require a lot energy to produce, so reusing it makes sense from that point of view. 24 GB of RAM is a very good amount, some new PCs don't have that much. RAM speed is not as important as the amount, so it being DDR3 is not really a problem in my opinion, it just limits how modern the next mainboard/CPU can be.

If it is a PC that is in active use I'd upgrade the GPU and call it a day.

For further reading and motivation, see https://solar.lowtechmagazine.com/2020/12/how-and-why-i-stopped-buying-new-laptops/

Sorry for the rambling and that none of this is really answering your question