tests: bluetooth: tester: Fix prov ctx init in PTS tests

This fixes regression introduced in
https://github.com/zephyrproject-rtos/zephyr/pull/63556



In the PR above `bt_mesh_init()` call was moved to `BTP_MESH_INIT`
command to allow to select alternative composition data when starting
the stack. AutoPTS sends `BTP_MESH_CONFIG_PROVISIONING` command
before `BTP_MESH_INIT` to prepare the provisioning context. But
because `bt_mesh_init()` is now called after
`BTP_MESH_CONFIG_PROVISIONING` command is sent, this configuration is
reset to the default which makes PTS tests to fail.

To solve this, this commit calls introduces a new command,
`BTP_MESH_START`, which will replace the original `BTP_MESH_INIT`
command. `bt_mesh_init()` will stay in `BTP_MESH_INIT` while the stack
will be started in `BTP_MESH_START` command.

Signed-off-by: Pavel Vasilyev <pavel.vasilyev@nordicsemi.no>