e2e: refactor initialization with single node logic (backport #1963)

[mergify]

This is an automatic backport of pull request #1963 done by Mergify.
Cherry-pick of 1da14b8 has failed:

On branch mergify/bp/v10.x/pr-1963
Your branch is up to date with 'origin/v10.x'.

You are currently cherry-picking commit 1da14b8b.
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Unmerged paths:
  (use "git add <file>..." to mark resolution)
	both modified:   tests/e2e/e2e_setup_test.go
	both modified:   tests/e2e/e2e_test.go
	both modified:   tests/e2e/e2e_util_test.go
	both added:      tests/e2e/initialization/init.go
	both added:      tests/e2e/initialization/init_test.go
	both added:      tests/e2e/initialization/node/main.go

no changes added to commit (use "git add" and/or "git commit -a")

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[p0mvn]

This required a manual backport so it's already in: #1975