Significantly improve the Libtask library using ideas from Mooncake / ReverseDiff

[mhauru]

TODO

Edit this issue with more details about what needs to be done.

Known issues

• Examples of a segfault with current Libtask: here and test/mcmc/Inference.jl segfaults on GHA Windows runner (sometimes) #2379 (comment)
• Performance degrades on Julia 1.11: Replace old Gibbs sampler with the experimental one. #2328 (comment)
• TracedRNG isn't deterministic even on the same architecture Reproducibility of particle Gibbs is not guaranteed on x86 #2446 (comment)

[yebai]

@willtebbutt and I have discussed this a few times during meetings. Will, can you add your plan here?