Database of parts with alternate numbers
What you are asking here is to have all possible part numbers for similarly looking elements. However, while both elements could look to be the same for you they may have significantly different properties.
Both Bricklink and Rebrickable have alternative numbers for the same mould, which is the case with the element in first URL. However, last two items are different elements - one has Thin support and the other comes with Thick support - which is why they are separated. It may be negligible for you, but someone else may find such difference essential.
Another approach would be to lookup by name - searching for &quot;Arm Mechanical, Exo-Force&quot; results in finding both elements, no matter if it is thin or thick version. Looking up by main properties (mainly size) can give you other, alternative elements as well. A good example here would be &quot;Brick 2 x 4&quot; - there is a classic 2x4 brick as well as some modified ones, that would all work fine when building, say a wall. But classic brick may not work if model utilize special properties of that particular modified version of 2x4 brick.
If your issue is with building MOCs that you found on Rebricklable you can adjust your building options. You can apply this permanently across the website in your setting page: Account &gt; Settings &gt; Building Sets/MOCs &gt; Ignore mold variations in parts.

Or you can apply this setting for particular Set/MOC: Build this MOC &gt; Change Build Options &gt; Ignore mold variations in parts