2002 YZ250 silencer confusion/ advice needed please...

Longer will smooth it out. Stock aint bad on a yz 250 i usually run stock ones these days

The X has a different head, CDI, and powervalve setup. You don't need to spend a bunch of money and copy these things though. I would start with retarding the ignition timing 1-2 degrees.

The whole short silencer = more bottom end is not entirely accurate. Outlet size matters more. What exhaust setup you running now? I would just stick with stock if you're looking for smooth delivery. After, that FMF Fatty is known as being very well rounded. Pick any silencer.

This is very solid advice right here.
You don't get much from changing the silencer, but you can really change the power spread with a small change to the timing.

The FMF fatty pipe is pretty good for drawing out the power and being super smooth on the YZ.
I run a Factory Fatty at at some of our local tracks where the corners are flat or off-camber and the soil is slick.

The PC pipe has a harder hit and pulls mid/top (probably not your flavor with the hit)
The Bills pipe is more low/mid oriented. (if you can learn to ride a gear higher, this pipe is the best).
The DEP pipes are a very good spread of power, similar to the Bill's pipe, but they pull harder toward the top.

I prefer the DEP and the Bill's when I race if the traction is good.

Jetting, timing, gearing and a flywheel weight are the best mods on the YZ (I don't run the weight).
Milling the head down a bit really helps too, but if you go too far it makes the bike too punchy at part throttle.

I have a completely stock. '01 YZ250 that I run with a stock pipe and silencer. the low end is amazing and I think over the years Yamaha has added a little too much volume to the head which almost mellows it out too much. The YZ250x has considerably less compression (different head) than the YZ which lessens the snap off the bottom. I don't know why you think a flywheel weight won't help but the hot ticket was to run an 8oz flywheel weight even in moto. For woods/playriding people would even go heavier. The YZ-x probably felt pretty docile compared to your '02 which was when the YZ250 motor was reaching its highest state of tune from the factory. Yamaha would continue to add volume to the head and richen the needle to prevent detonation which did soften the motor a little. The powervalve is controlled via centrifugal ball governor and is not pressure operated. Pipes work in mysterious ways and one size doesn't fit all. As mentioned, the "shorter" silencer is snappier but gives up revs holds is somewhat true but not always. retarding the ignition slightly can mellow it out and I like the stock pipe best for overall smoothness but an FMF factory fatty would probably be second. Silencer-wise the stock silencer will probably be the most mellow. Oh....and I hear a flywheel weight works well.

I have a standard size silencer for sale in case you're interested.

https://www.vitalmx.com/forums/For-Sale-Bazaar,26/2002-2020-YZ250-FMF-T…

The silencer is a comparatively minor part of the equation if you're talking about power characteristics.
The 02 has different port timing and head dimensions to the new models. It was an impressive grunty engine which hits hard.
If you don't want to modify engine components, go with a flywheel weight, a standard pipe and silencer and try adjusting the timing. After you try that and if you still want it more mellow, you can always put a slightly thicker base gasket on the cylinder.

Try going down one tooth on the rear as well; that will soften the hit and as a bonus you can stretch out each gear a little longer.

Bottom end power and the ability for a bike to lug down low are two different things and often get confused.

In tight nasty terrain you want a bike that you can ride at low RPM without stalling and is smooth on the bottom with no abrupt hit. That’s what some consider good bottom end power.

On the other hand with a 450 for example you can come out of a corner at a low RPM and the strong bottom end power will pull you hard out at the twist of the throttle.

Having had a YZ 250 I believe what your looking for is a flywheel weight. It’s relatively inexpensive and an easy mid to do.

Retard the timing a degree or two.

YZ250 Timing thread

This^^, plus a 13oz FWW made for a super lazy bottom end on my 2016. I couldn't stand it after awhile, and went 8oz and stock timing.