Remove CI Caching step

[notmandatory]

Describe the enhancement

It looks like in our CI jobs the saving the cache step is taking longer than building and running all the test steps. If we can confirm this then we should re-configure our remove caching. The only thing that may make sense to continue caching is the bitcoind and electrsd binaries.

Use case

If caching isn't really speeding up the builds then we can get CI jobs done faster without it. Faster CI jobs means faster feedback to PR developers.

Additional context

See example run:
https://github.com/bitcoindevkit/bdk/actions/runs/11132332339/job/30941326509

[notmandatory]

Maybe rather than caching the bitcoind and electrsd binaries we can create a docker image with them and setup in the runner's env. Or use the nix dev shells from #1320.