OK, not much feedback as of yet, but continuing my journey anyways as that small PSU fan is really irritating when the room is all silent.
First I did some stress testing. I have a hard time to have the power supply draw more than 120W continuously from the wall outlet. Maybe a peak to 140W at some point, but that's about it. I still need to expand the system with 64 GB of RAM (instead of 8 GB RAM right now), and a more beefy SSD (WD Black SN850X), but I don't expect the power consumption to increase dramatically after those upgrades.
Even though the power supply is powering this system with two fingers up the nose (google it), and probably I could just discard the fan altogether, I don't want to mess with the airflow in this tiny system too much, so I'm taking route 1. Ordered a ebm-papst 612 NGLE low-noise (>20 dB) to replace it. While I am at it I also changing out the (unusual sized) Foxconn case fan for something a bit better and probably even more silent: NoiseBlocker NB-BlackSilent Pro PC-P 80×15mm.
And since everything has to come out anyway when removing the power supply, I'm going to repaste the CPU as well (Noctua NT-H2). I will not replace the CPU cooler (yet) as I think it's silent enough and good in dissipating the heat to the back of the case with that black duct (https://i.dell.com/is/image/DellContent/content/dam/ss2/product-images/dell-client-products/workstations/fixed-workstations/precision/3460/media-gallery/desktop-precision-3460-gallery-8.psd?fmt=pjpg&pscan=auto&scl=1&wid=4004&hei=2919&qlt=100,1&resMode=sharp2&size=4004,2919&chrss=full&imwidth=5000).
If everything goes to plan I'll probably do all these upgrades in the next week or two. I'll log it here, just in case some other 3460 owner is interested in my story.