Adapt `NeptuneLogger` to new `neptune-client` api (#6867)

* Initial split to NeptuneLegacyLogger and NeptuneLogger

* Adapt NeptuneLogger to neptune-pytorch-lightning repo version

* Fix stylecheck and tests

* Fix style and PR suggestions

* Expect Run object in NeptuneLogger.init

* Model checkpoint support and restructured tests

* Reformat code - use " instead of '

* Fix logging INTEGRATION_VERSION_KEY

* Update CHANGELOG.md

* Fix stylecheck

* Remove NeptuneLegacyLogger

* updated neptune-related docstrings

* PR suggestions

* update CODEOWERS file
* move import logic to imports.py
* minor neptune.py improvements

* formatting fixes and minor updates

* Fix generation of docs

* formatting fixes and minor updates

* fix

* PR fixes vol. 2

* define return type of _dict_paths method
* bump required version of `neptune-client`

* Enable log_* functions

* Update pytorch_lightning/loggers/neptune.py

Co-authored-by: Adrian Wälchli <[email protected]>

* Revert "Enable log_* functions"

This reverts commit 050a436899b7f3582c0455dc27b171335b85a3a5.

* Make global helper lists internal

* Logger's `name` and `version` methods return proper results

* Initialize Run and its name and id at logger init level

* Make _init_run_instance static

* Add pre-commit hook code changes.

* Fix blacken-docs check

* Fix neptune doctests and test_all

* added docs comment about neptune-specific syntax

* added docs comment about neptune-specific syntax in the loggers.rst

* fix

* Add pickling test

* added myself to neptune codeowners

* Enable some of deprecated log_* functions

* Restore _run_instance for unpickled logger

* Add `step` parameter to log_* functions

* Fix stylecheck

* Fix checkstyle

* Fix checkstyle

* Update pytorch_lightning/loggers/neptune.py

Co-authored-by: thomas chaton <[email protected]>

* Fix tests

* Fix stylecheck

* fixed project name

* Fix windows tests

* Fix stylechecks

* Fix neptune docs tests

* docformatter fixes

* De-duplicate legacy_kwargs_msg

* Update .github/CODEOWNERS

Co-authored-by: Adrian Wälchli <[email protected]>

Co-authored-by: kamil-kaczmarek <[email protected]>
Co-authored-by: Adrian Wälchli <[email protected]>
Co-authored-by: thomas chaton <[email protected]>