My 2 candidates for quietness would be the Olympia SM9 and the Royal 10.  Both are clean, adjusted, and as far as I know they have the original rubber on the platen.  It seems to me it's more to do with how sturdy the frame is, and the precision and robustness of the moving parts.  There is also padding to some extent.

I've had 2 experienced typewriter techs, one has a repair shop for over 30 years and the other one has a service and platen recovering business, mention that some of the older wood core platens had lead in them for noise reduction.  Royal used this strategy.  If an old platen has bulges in the rubber, it is more than likely the lead has gone or is going to lead oxide. I can't say what  all brands or models used lead, but it seemed to be an industry wide practice before the cores went to metal during the 1950's.

Rubber is a big factor in reducing the familiar clacking.  90 to 92 Shore A was the spec'd hardness and after having some platens recovered; they were quieter at that hardness than the more brittle original covering..

You need to use that SM9. I think it actually gets overlooked because it's so darn competent, it seems a little bland. But really, if I could only keep one machine, it might be the one.

Haha
I know that in many regards the Olympias are probably second to none,
but at least The SM 9 that I have, it just doesn't do it for me...
I prefer the Erika
Or a QDL

But I am definitely going to get another Olympia eventually, probably one of the ultraportable's, or maybe an earlier SM model. SG will be in Running as well

My quietest typewriter is the Continental Silenta, and by a long shot. Everything is designed to get rid of the noise, and in fact you won´t hear the typeslugs hitting the platen at all.
At least in theory a noiseless typewriter should be quieter than a regular one, but there are "normal" machines which are pretty silent as well.

I agree with Olympias being silent. If properly tuned the carriage goes like the wind and most of the operation isn´t that noisy either. But Erikas... My S&N Erika S is a screaming beast because the typeslugs hit the platen at supersonic speed and the platen itself is harder than it should, too. Another screeching monster is the Smith Corona Electra 220. More than a motor it sounds like it has an V8 engine under the hood, not to mention (again) the sheer hatred the typeslugs hit the platen with.
On a less conventional note, the Regia Mixta (Spanish design!) is very noisy as well, because the machine itself acts as a resonance box when typing.

Back to more silent typewriters, the Olivetti Linea 98 isn´t that drilling, either. And do electronic typewriters qualify for this? The Olivetti ET2200 is a good example of a large wedge, and is quiet enough.