I had new bearings installed on the bottom end. I also installed a new oil pump. $$$$

Almost no change from before.
(ONLY when eng temp is cold, does the oil pressure gauge on the dash indicates what was described above as "normal" . My mechanic says he verified the oil pressure hence, sending unit is okay with a mechanical gauge and it is reading 8psi when idling at warm, but the dash still shows zero. When engine is hot and I rev the engine or drive hwy speeds the dash needle moves up only slightly.)
Next, the mechanic is suggesting to replace the timing chain tensioner, as it might be a source of internal oil pressure loss/leakage. I'm over my head here...

Is this engine 'done for'?
Anyone had similar experiences? What internal leaks could be causing low oil pressure readings? What will changing the timing chain tensioner accomplish?
thanks in advance for any advice...