[unstable2507] Backport #10311: [Staking] Async Election and Export

[paritytech-release-backport-bot]

Backport #10311 into unstable2507 from Ank4n.

See the documentation on how to use this bot.

[paritytech-release-backport-bot]

Please cherry-pick the changes locally and resolve any conflicts.

git fetch origin backport-10311-to-unstable2507
git worktree add --checkout .worktree/backport-10311-to-unstable2507 backport-10311-to-unstable2507
cd .worktree/backport-10311-to-unstable2507
git reset --hard HEAD^
git cherry-pick -x 90b7cafd8cfba509cc0f6ea476acc1a8c9ad0c11
git push --force-with-lease

[paritytech-workflow-stopper]

All GitHub workflows were cancelled due to failure one of the required jobs.
Failed workflow url: https://github.com/paritytech/polkadot-sdk/actions/runs/19937384581
Failed job name: test-linux-stable

[Ank4n]

@EgorPopelyaev Can this be merged as well (and published)? I think there is plan to make a new release with unstable2507 and we would like this as well as @lexnv's elastic scaling changes to go live soon/together. cc: @TorstenStueber