[client] Refactor context management in ConnMgr for clarity and consistency

[pappz]

In the conn_mgr we must distinguish two contexts. One is relevant for lazy-manager, and one (engine context) is relevant for peer creation. If we use the incorrect context, then when we disable the lazy connection feature, we cancel the peer connections too, instead of just the lazy manager.

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• [x] Is it a bug fix
• [ ] Is a typo/documentation fix
• [ ] Is a feature enhancement
• [ ] It is a refactor
• [ ] Created tests that fail without the change (if possible)
• [ ] Extended the README / documentation, if necessary

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[sonarqubecloud[bot]]

Quality Gate passed

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0 Accepted issues

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0.0% Coverage on New Code
0.0% Duplication on New Code

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