Enforce member variable naming schema

### What

To my understanding (may be this needs clarification @NicolasFussberger ), we are using this naming schema for member variable
`my_member_variable_`

However in alive_monitor code (and most probably also somewhere else) for historical reasons there are also other styles used, like `m_recovery_client` or `_my_member_variable`.

So the task here is to unify this with a clang-tidy rule. Also make sure that introduction of wrongly named variables is not possible. Normally this should work out of the box, as clang-tidy is executed as pre-commit hook.

### Acceptance Criteria (DoD)

- Unified naming schema
- Introduction of invalid named member variables is impossible (as long as precommit hook is not skipped)

### How

_No response_

Start by locating the clang-tidy configuration and pre-commit hook, then inspect member-variable naming in the alive_monitor code and elsewhere. Confirm the intended trailing-underscore schema and the full set of existing variants with the maintainers. Done means existing member variables are unified and the hook rejects newly introduced invalid names.

Written by the indexing model from the issue text.