as mentioned, that's a spacer only added to later t5's.....rebuild kits include now, but it's only to help oiling, and not essential.
your issue is likely the throwout bearing. that's why the noise goes away with the clutch pedal depressed.
If it's not the t/o bearing, then it's a bad bearing in the t5,...one of those two are your issues.
if the noise goes away with partial clutch pedal effort, then it's a simple clutch adjustment.....your clutch adj would be too loose. If it goes away with only full pedal press, then I'd try swapping the t/o bearing first before taking the t5 apart again.
Generally whining is pretty bad. IMO, most cases involve more work than a T5 is worth.
Figure if it grinds or pops out of gear, a rebuild with parts and labor is about $550 give or take a few bucks.
Nothing in the small parts rebuild kit is going to fix a whine more than likely.
So now you get into replacing major components of the trans, which are generally very expensive.
I had a trans that was whining, hanlon quoted me $850 to fix it.
So i got a $100 trans that was popping out of gear, and had it repaired, total was $600 (including the trans).
A T5 is very easy to rebuild at home. Buy the video from Hanlon on how to do it. You are looking at about 130 in parts to do a good job. Use the video to tar down and inspect the T5 before you get a rebuild kit. That way you know what your T5 needs before you shop.