refactor: remove all deprecated code

[mrossinek]

Summary

This commit removes all deprecated code. Even though this is done a bit earlier than originally announced under the Qiskit deprecation policy, we are taking this step now since this project has become part of a community effort. As a direct consequence, new codeowners will soon join the team behind Qiskit Nature. Rather than handing over a codebase that includes pieces of code which need attention in the near future (and even continued support until then) we are removing these parts early.

As a consequence, if you still require parts of this code, we suggest you stick to Qiskit Nature 0.6 until you can transition based on the provided migration guides.

This commit also removes the deprecation utilities which are superseded by the ones provided by Qiskit directly (see qiskit.utils.deprecation). Thus, this PR closes #1196

Details and comments

• [x] add a release note with a prelude section to explain the above

[mrossinek]

This also closes #1169

[mrossinek]

Since there is too much to go through in detail in this PR, here are a few noteworthy details:

• I removed the deprecation utils (see prior comments)
• I removed all occurrences of opflow (this includes PauliSumOp)
• I removed all factories and their usage
• I removed the QubitConverter and all its usage
• I removed the runtime module
• I removed all the settings attributes which become unused as a result of all these removals
• please have a look at the suggested prelude in the release note

[woodsp-ibm]

What do you want to do about the AdaptVQE howto docs/howtos/adapt_vqe.rst It refers to settings that this removes. I get that it will also need to be updated around qiskit_algorithms but this PR removes some of what it refers to, so if we want it in sync with this then maybe update it here - and again for the algorithms change later.

[mrossinek]

What do you want to do about the AdaptVQE howto docs/howtos/adapt_vqe.rst It refers to settings that this removes. I get that it will also need to be updated around qiskit_algorithms but this PR removes some of what it refers to, so if we want it in sync with this then maybe update it here - and again for the algorithms change later.

Nice catch! I did not think to look through the tutorials and how-tos for additional usage of settings or other removed aspects. Will do that now :+1:

[mrossinek]

I have pushed two additional changes:

• removing all further usage of setting attributes which have been removed. Grepping for settings now only shows results for optimize_einsum and in the migration guides (where they should remain)

• I removed the release note which was added in #1142 because it is now obsolete