Split off doctests from main tests

[Swiddis]

Description

Following in the footsteps of #3070, this PR splits doctests into its own step too. The general motivation behind both changes is that both suites can start failing due to factors outside this repo (doctests if CLI changes, BWC if lucene codec changes), but integ tests should always pass. Since issues were recently caused by missing failing integ tests (hidden by doctest/BWC failures that were unrelated to the changes), having them in their own checks to make integ test failures visible at a glance would have prevented the issue. It also makes the actions run faster.

Related Issues

N/A

Check List

• New functionality includes testing.
• New functionality has been documented.
• New functionality has javadoc added.
• New functionality has a user manual doc added.
• API changes companion pull request created.
• Commits are signed per the DCO using --signoff.
• Public documentation issue/PR created.

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