release-25.2: restore: fix split race in split and scatter processor

[msbutler]

Backport 1/3 commits from #147104.

/cc @cockroachdb/release

---

Informs #146083

Release note: none

[blathers-crl]

Thanks for opening a backport.

Please check the backport criteria before merging:

• Backports should only be created for serious
  issues or test-only changes.
• Backports should not break backwards-compatibility.
• Backports should change as little code as possible.
• Backports should not change on-disk formats or node communication protocols.
• Backports should not add new functionality (except as defined
  here).
• Backports must not add, edit, or otherwise modify cluster versions; or add version gates.
• All backports must be reviewed by the owning areas TL. For more information as to how that review should be conducted, please consult the backport
  policy.

If your backport adds new functionality, please ensure that the following additional criteria are satisfied:

• There is a high priority need for the functionality that cannot wait until the next release and is difficult to address in another way.
• The new functionality is additive-only and only runs for clusters which have specifically “opted in” to it (e.g. by a cluster setting).
• New code is protected by a conditional check that is trivial to verify and ensures that it only runs for opt-in clusters. State changes must be further protected such that nodes running old binaries will not be negatively impacted by the new state (with a mixed version test added).
• The PM and TL on the team that owns the changed code have signed off that the change obeys the above rules.
• Your backport must be accompanied by a post to the appropriate Slack
  channel (#db-backports-point-releases or #db-backports-XX-X-release) for awareness and discussion.

Also, please add a brief release justification to the body of your PR to justify this
backport.

[cockroach-teamcity]

This change is 

[msbutler]

blathers backport release-25.2.1-rc