Module API documentation is described in Doxygen comments in C/C++ files
in src/ directory. No sense to run this job for other changes. The patch
changes paths in workflow accordingly.

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(cherry picked from commit 9af36ae1)

The condition for workflow concurrency was fixed in accordance with
the new name policy for supported branches (2.10 -> release/2.10,
2.11 -> release/2.11).

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(cherry picked from commit 0c117197)

- Rename the workflow into `publish-module-api-doc` to be consistent
  with other workflow names.
- Refactor workflow triggers.
- Run the workflow only on push to the tarantool/tarantool repository
  or on pull request if the 'notest' label is not set.
- Simplify condition for publishing generated API documentation.

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(cherry picked from commit c9e0074d)

Follows up #8194

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(cherry picked from commit 07d686dc)

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(cherry picked from commit 140e2c16)

The 1.10 branch is not supported anymore and there is no need to keep
the logic for it.

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(cherry picked from commit e0c5a41f)

* Prepare workspace before actions/checkout to prevent
  git-related workflow failures.
* Replace tarantool/actions/cleanup, because it solves
  just the same problem.

Resolves tarantool/tarantool-qa#285

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Fix the following warning:

NO_WRAP
    Node.js 12 actions are deprecated. For more information see:
    https://github.blog/changelog/2022-09-22-github-actions-all-actions-will-begin-running-on-node16-instead-of-node12/.
    Please update the following actions to use Node.js 16: actions/checkout
NO_WRAP

Fixes tarantool/tarantool-qa#279

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`make api` generates `src/module.h`. `make module_api` is the target for
compiling a library for testing of the module API:
`test/app-tap/module_api.so`. It depends on the `api` target.

Both works for generating `module.h`, but `make api` don't do extra
unneeded actions.

NO_DOC=Not a user visible change.
NO_TEST=It is CI workflow. It would be too strong to test each part of
        the testing/deployment infrastructure.
NO_CHANGELOG=Not a user visible change.

See d3f32d18 for explanation.

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Publishing workflow will run building module API documentation for
opened or reopened pull request with label "full-ci" and will publish
documentation on Github Pages on push to the master branch.

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This patch allows to call `report-job-status` action with only one
input: `bot-token`. VK Teams chat ID has the default value in current
action, API URL has the default value in [1].

[1] `tarantool/actions/report-job-status`

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This patch introduces the new `report-job-status` action that is used
for sending notifications to the VK Teams messenger on the job failure.
It replaces the old `send-telegram-notify` action sending similar text
notifications to the Telegram messenger.

The new action selects the corresponding chat for the notification on
failure and uses the `tarantool/actions/report-job-status` action [1]
for sending it to:

* the team chat (Tarantool CI/CD reports) - if the job started on any
  event in the master or release branch (1.10, 2.10, etc);

* a personal chat (created by the committer) – if the job started on
  creating/updating a pull request or any event in other branches.

[1] https://github.com/tarantool/actions/tree/master/report-job-status

Resolves tarantool/tarantool-qa#258

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- Fix checkout with submodules
- Fix publish action version

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