Automatic merge from submit-queue (batch tested with PRs 66577, 67948, 68001, 67982). If you want to cherry-pick this change to another branch, please follow the instructions here: https://github.com/kubernetes/community/blob/master/contributors/devel/cherry-picks.md.

Refactor volume test in a similar way to csi tests

Refactoring for non-csi e2e test similar to below commit in csi e2e test.
https://github.com/kubernetes/kubernetes/commit/4d11dab272fc358c918a1a6b83db8f938535cdb0#diff-0d9ecaa3e6a0297186ad33f57aad472e

Scopes for this refactoring are below three files:
  - test/e2e/storage/volumes.go
  - test/e2e/storage/volume_io.go
  - test/e2e/storage/persistent_volumes-volumemode.go



**What this PR does / why we need it**:

**Which issue(s) this PR fixes** *(optional, in `fixes #<issue number>(, fixes #<issue_number>, ...)` format, will close the issue(s) when PR gets merged)*:
Fixes #66571

**Special notes for your reviewer**:
/sig storage
@davidz627 @msau42 @jsafrane  

**Release note**:

```release-note
NONE
```