The engine is cold in both of those videos.
Coolant seems to be fine.
The odor of the exhaust does not seem to be that of coolant. It has an acrid odor, not a sweet smell.
Also, since my initial post, I have noticed an oil leak. Saw it after I made the videos.

Is there a PCV valve on this engine? I do not see it if there is one. However, the parts sellers all list one for it.

Did you even look at the manual I posted for you. It has all the info you are asking about.

if its like the LN3 3800 (pre series 1) its under the fuel rail on the passenger side of the intake, in the intake, very annoying to access

That'* where it was. Thank you for your comment. I removed the accessory belt and lifted up the alternator to access it. I am replacing it, but it does not seem to be clogged at all. So I am doubtful it is the problem.

I thought it may be the EGR Valve, but I do not see one in the parts list or the schematic for this engine.

I believe the 3300 does not have an EGR valve.

Bypass your Evaporative emissions system, and unplug the solenoid connector and then drive your vehicle. report back results.

Also confirm the transmission modulator isnt the original, take a picture of it (its down in the engine bay by the evap canister but downlow. has a vacuum line to it)

my bad, the skylark is using a THREE SPEED? thats just gross, but it appears you do not have a modulator, as you found out earlier in this discussion. Does it have a TV cable?

The 3.3 has a throttle cable assembly that appears to be close to the 3800 in 1988-1991
If it is, the tv cable might adjust the same way. There appears to be 2 types of tv cable for a 93 skylark, my guess is the smaller engine option uses one
Watch this video where i linked it, does your tv cable look like this? if so, check its adjustment

I believe I solved it. Before replacing the injectors, I had a misfire without codes. I confirmed that one of the injectors was leaking, so I replaced all six. it turns out that the new injectors were defective and were flooding the crankcase with gas. I've replaced those now and am hopeful that this will resolve the problem.

Cheap parts suck

But glad you figured it out
If they are in ok physical shape, i plan to only send out my injectors who will flow test and rebuild them