Can’t you drill out the top cap screw? It’s aluminium, so should be relatively easy to drill and since you don’t care about the compression plug it doesn’t matter if you aren’t perfectly centered. Just make sure you start centered (i.e. use a centre punch).

Otherwise I guess you could also try to hammer down on the remains of the screw to push it through and open the compression plug. But maybe not really advisable with a carbon tube.

Thanks for all your help!

What worked

Drilling with a small bit into the edges of the broken top cap screw.
Miraculously, I noticed that the screw loosened itself as it's unwinding little by little from the vibration of the drilling.
Then I used some pliers to unwind it out and was able to find a near-perfect hexagon hole where I can stick my 6mm in.

Mis-diagnosis?

So...the top cap screw thread doesn't seem to be burred or damaged. Even cosmetically it looks fine.
The black anodising on the thread is consistent and no bubbles or cracks can be seen.

But I'm actually really curious, and want to prevent this from happening again!
Please leave your thoughts below so we can learn more from my mistake together.
Did I start the drillium too early? Was there another solution?

TLDR;

1. Loose headset, and top cap bolt stuck.
2. T25 top cap bolt stripped.
3. Araldite in the bolt and on my T25 key, left it over 2 nights, didn't unscrew.
4. Top cap bolt is aluminium, compression plug bolt is steel.
5. Drilled off top cap, left an even more stuck top cap bolt in compression plug.
6. Drilled out top cap bolt, bolt seems perfect.
7. Please tell me why top cap bolt is even stuck in the first place.

Thanks @Michael and @Carel.
Guess drilling really helped in the end!

Analysis:

Well done for getting the items out and sharing the progress. Based on your success photos, the topcap is not suitable for the forces placed on it because the ultralight topcap is what broke.

From the Top-cap linked website I read these specs:

Option 1:

• ABSOLUTEBLACK, Headset top cap, One piece cap and bolt
• Description Do not fit "exspanding" star nuts
• Material 7075 aluminium, CNC machined
• Color Black
• Weight 4 g

Based on the Aliexpress photo you have an expanding compression-style plug, not a star nut as warned off in the description, so one presumes it should be okay.

What I don't understand is why this top cap is stated to not work with a star nut. This leads me to wonder if the compression plug shares some similarities with a star nut such that this top cap is over-stressed.

A star nut does the same task, and I presume has less movement than the rubbery bumpers of the compression plug. Whether that was the cause or not, hard to say.

Option 2: You got a faulty one - some pre-existing damage to the bolt, or a void, or even bad packaging and transit could have pre-weakened the threads. They're only aluminium, so once bent will not straighten.

Option 3: Assembly problem - anodised aluminium tends to slide quite nicely, but raw aluminium doesn't. Could be the inside of the plug's thread was raw, and the anodising rubbed off while tightening, leaving the two surfaces to bind and gall together. As you add torque, the threads lock up and the aluminium bolt gives way.

And the steel thread is stronger than the aluminium one. Perhaps using assembly lube may have stopped this from happening.

Solution: I'd suggest using a regular top cap and steel bolt. If money's no object, a Titanium one has weight-weenie credentials twice over (weight off your bike and off your wallet :-