Computer fan and street noise are in every quiet vocal take, what do people actually do in a normal room?

Measure before you buy or process anything, because you have at least three different problems in that list and they have different fixes.

Record thirty seconds of silence, nobody in the room, everything running as it normally does - and look at it. Then repeat with the computer off, then with the fridge unplugged for a minute. Three files, and comparing them tells you which source is actually dominating rather than which one you notice.

Most people are surprised. The fan is usually not the biggest contributor; the low rumble from traffic and appliances is, and it is inaudible as a sound while being very present in the file.

Then fix in this order, because it is cheapest first and each step makes the next less necessary:

Move the microphone, not the noise. Every doubling of distance from a noise source drops it substantially. Turning ninety degrees so the microphone's dead side faces the computer often does more than anything you can buy, a cardioid pattern rejects the rear strongly, and most people have the machine directly behind them without thinking about it.

Get closer to the source. Closer to the microphone means more signal for the same noise, which is the whole ratio. Half the distance is a large improvement, and it costs nothing.

A high-pass filter removes rumble that is below anything your voice or guitar produces. This is the one processing step that is not a compromise.

The fridge is the easiest one on the list and nobody mentions it: switch it off at the wall for the take. Twenty minutes does nothing to the food and it removes a compressor you cannot process out.

Set a timer on your phone. Ask me how I know.

On the computer specifically, since you said moving it is not easy: it is usually easier than it sounds and it is the single biggest win available.

The options in ascending order of effort:

A long cable. A USB extension or a longer monitor cable and the machine goes on the far side of the room, behind furniture, or out of the door. Two or three metres of distance is a large reduction.

Point it away and put something soft between. Even a duvet over the back of a chair between you and the machine helps at the frequencies fans produce.

Stop it working during takes. A lot of fan noise is the machine doing something it does not need to do - a backup, an indexer, a browser with forty tabs. Fans that spin up during recording are usually responding to load you can simply not create.

Fix the fan curve if it is a desktop you control. Many run far more aggressively than they need to at idle.

On the fridge and the traffic: those need mass, not foam, and mass is what you cannot do in a rented bedroom. What you can do is time it. Record when the road is quiet and unplug the fridge for the take, with a note on the door so nobody wonders. That sounds unserious and it is what a lot of people actually do, because it works completely and costs nothing.

A gate does not remove noise, it removes the gaps between the noise. That distinction took me a year.

A word on the processing side, since you found the plugin makes things worse when pushed: that is not you using it wrong, that is what it does.

Broadband noise reduction works by identifying the noise and subtracting it, and it cannot subtract only the noise. Push it and it takes the quiet detail of the performance with it, which is the underwater sound you heard. It is genuinely useful at a light setting on a problem you could not prevent. It is a poor substitute for not recording the noise.

What is worth doing at the mix instead:

High-pass everything that does not need low end. Most rumble lives below where a vocal starts, and this is free.

Ride the level or use a gate gently so the noise is not sitting there during pauses. A lot of what people find objectionable is the noise floor appearing in the gaps rather than under the performance, and simply silencing the gaps handles it.

Be careful with compression. You noticed this yourself: compression raises the quiet parts, and the noise is a quiet part. A slightly less compressed vocal often sounds cleaner than a heavily compressed one that has been denoised afterwards.

And the general principle worth keeping: the noise floor is set at the moment you record. Everything after that is damage limitation, so the ten minutes spent moving the microphone is worth more than any plugin.