Use new VM Runtime API (#34961)
### Details:
- Use the "new" VM Runtime API as it is implemented in
https://github.com/intel-innersource/applications.ai.vpu-accelerators.vpux-plugin/pull/25234.
Tested by
https://github.com/intel-innersource/applications.ai.vpu-accelerators.vpux-plugin/pull/25235
### Tickets:
- *E#204028*
### AI Assistance:
- *AI assistance used: yes*
- *Renaming of functions, structs, enums.*
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Signed-off-by: Skrebkov, Artemy <artemy.skrebkov@intel.com>
