test: lwm2m: Fix minor timing issue

RD client tests work well on emulated (fast) environments
but tend to fail on real HW with real time sleeps.
This change refactors wait_for_service() to be a bit more
syncronous on background service, instead of relying hardcoded
sleeps.

Fixes #61824

Signed-off-by: Seppo Takalo <seppo.takalo@nordicsemi.no>