I have a be quiet! Pure Base 500DX (which has a mesh front) and three Silent Wings 3 140mm PWM High-Speed fans, also from be quiet. Two front intakes, one rear exhaust. Top of the case is closed with a noise insulated top. The fans are installed with rubber mounts and pushpins to minimize vibrations.
Due to the optimized airflow of my case, and it being overall more cramped than your average midtower, I'm able to keep my intakes at 800rpm max and my exhaust at 900rpm during gaming. The fan on my CPU cooler, the NH-D15S Chromax Black, is also about 600-900rpm. All of this keeps both my GPU and CPU under 65C even in a demanding game.
The fans, due to how they're made and the mounting mechanism used, are incredibly quiet. My case fans are now as loud in gaming as my previous case fans were at idle. Meaning very quiet.
Before getting these case fans, my old Pure Wings 2 (which are low end fans not suited for a build like mine) had to spin up to 1000-1100 RPM to keep my components cool, and even at 900rpm the noise bothered me. No rubber mounts, no rubber frame, and it being installed with screws also sent a ton of vibrations through my case, amplifying noise. It was unbearable, even making me put off gaming sometimes and just go to YouTube. Not anymore with these new fans though.
===
Takeaway here is if noise bothers you, the main offender is the case fans. If you get some quality case fans built for silence (like the Silent Wings 3), and configure a more relaxed fan curve, you can find a balance of GPU cooling performance and noise. My gaming experience has been considerably improved when my PC no longer sounds like a jet engine (who would've thought?)
140mm > 120mm when it comes to both noise and cooling performance. Larger fans don't need to spin faster to move the same amount of air as a 120mm fan, thus being quieter.
Of course, if you took off your side panel and the GPU temps didn't improve at all, then the heatsink/fans on the GPU are just not enough to cool the GPU. This was the case with my Zotac 2070 Mini. No matter the airflow configuration, that card always went to over 80C in demanding titles. The massive heatsink and six direct-touch heatpipes on my 3070 Gaming X Trio even allows the GPU to be passively cooled without the fans needing to spin in some modern games maxed out at 1440p.
One more thing, I feel that your ears are more important than your GPU temperatures. If you have to lower case fan RPM to reduce noise, but make GPU temp be a bit higher, do so. Those components can take the heat for years, but you will drive yourself crazy listening to the noise for years. I've also found that RPMs above 1000 do not do anything to the cooling of my components, except introduce unneeded noise. So there are diminishing results here, find the perfect fan RPM for your configuration.
