[Process] Use a consistent way to reset data of the process latest run

It is actually useful when cloning or running again a process.
merged branch romainneutron/properties-reset (PR #8806)

This PR was merged into the 2.2 branch.

Discussion
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[2.2][Process] Use a consistent way to reset data of the process latest run

| Q             | A
| ------------- | ---
| Bug fix?      | yes
| New feature?  | no
| BC breaks?    | no
| Deprecations? | no
| Tests pass?   | yes
| Fixed tickets |
| License       | MIT

It is actually useful when cloning or running again a process.

Commits
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0723c10 [Process] Use a consistent way to reset data of the process latest run