Why not use eBPF instead? Then you could see all http requests from all processes at once, including ones that are already running. Plus you wouldn't need to bother with TLS at all, just hook on e.g. write(2).
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You need the kind of CA certificate trick that httptap uses. It comes with its own set of caveats (e.g. certificate pinning), but it can be made to work reliably in most practical scenarios.
I've spent an unjustifiable amount of time thinking about this specific problem building Subtrace [1], so I'm genuinely very interested in a simpler / more elegant approach.