Mellowness

Yes, if you have Standard, reducing hammer hardness can do a lot to soften the piano sound. Also reducing the hammer noise may help, if you don't like too much of the 'thump' which can vary according to preset. And yes, reverb too. Some presets have a dry studio reverb which can seem a bit harsh - try changing it to one of the halls and adjust the mix level to taste.

All those are great ways to get softer sounds.

I'd begin with presets like "New Age" and "Dreamy" or "Cinematic".. they are pretty gorgeous - even if not your own ideal, they are likely to have settings to 'view, consider, remember and apply' to other presets.

Don't overlook the compressor if it suits your outcome (it can allow soft playing and clip attacks - it's often a substantial component of what people hear as a good piano sound on recordings - this is not a realism thing - but a "make my piano preset seem more like something I heard on an album". It's doable with a little time loading compressor presets, hearing differences, making some slider adjustments you like, and saving your own presets to try with any other pianos.. you get your own fav ones pretty much the way you like over time - same with any audio tool really).

Also lower 'hammer noise' to reduce some attack to go with dazric's suggestion to lower 'hammer hardness'.

Plus - the new 'Note effects' tools.. take a little or a lot of attack off there. A small number in the 'Attack envelope' (bottom right of its pane).. you now don't have an aggressive attack - and indeed you could make your attack very slow and long, like in some 'bowed' presets.

Using layers creatively can become a joy, and certainly adding a 'bowed' kind of layer to an existing soft piano can create many interesting soft sounding instruments.. unlimited in variations, all up to our own imaginings. And not too hard to learn compared to some very strangely difficult tools which do some much more simple things out there.

Other things... load an EQ preset (Equalizer on main interface, or 1 or more EQ3 insances in the FX section) to find ones which make the defaults softer with fluffier bass.

Like Stephen mentions (lower the top possible velocity in the curve setting), you can also create a steeper curve at the lower region, to scoop out there.. if the lower region is a lower curve, you play as normal but hear softer tones when playing at lower velocities. Some may just not know this - and others will think it's a fundamentally incorrect thing to do.

To me, there's no 'correct' curve (or piano sound.. only what we wish to hear, sometimes for a piece, other times for a daily practice piano etc.) - but indeed velocity curve can shape any piano from default to bright or dark in good ways, with subtlety or drastic differences.. again though, like always - users have to play around with it to find their best uses of the velocity curve, and it may take time and coming back to it over time, before you genuinely know you like your changes - nothing automatic can solve for that, it's a human to machine setting which can make a default piano seem set up way softer or brighter.

Depending on how creative you wish to get, you can load several Delays in the FX section too (lower their tone a little for softening) - give them each timings which may work at the tempo you desire. On 1 of them, click the small green LED button to swap channels - those delays may sit better in the mix.. alter until you have some glittery fading multiple gentle echos.. it's not something to do unless getting beyond a plain piano in the room sound of course - but plenty of etherial piano sounds people talk about as being really sweet may have all kinds of subtle non-realism based sugar coatings which give it a unique sort of 'it factor'.

In the main Equalizer (button on right side, front interface), drag the bass up 1 or 2 decibels, and drag the treble dot down similar amount. A basic tilt can offer just an immediate sense of 'more surrounding soft bass' and less 'treble brightness' on any preset. It's a starting point kind of thing - and ideally you might find you like to save a certain number of your own fav Equalizer presets to re-use, subtle or strong.

But definitely - Pianoteq delivers a quite realistic piano dynamic. I think this is likely the main thing users either feel is 'different' to many other products, or harsh.

The defaults are quite stable in my exp. and you can push them dramatically in any direction with some editing.. but if Pianoteq put out 'less realism' and more 'dripping in production values' presets, maybe it would lose many pianists seeking 'realism first'.

But, the FX and other tools in Pianoteq can allow you, without too much fuss in the scheme of things, to edit any preset in unlimited ways, subtle or dramatic.

Anyone wanting more will likely be accustomed to available tools in their DAW for achieving something akin to their own production values and desires.

Watching a bit of Simeon Amburgey's demo, timbre is really nice! I like it a lot. I think some of the previous suggestions are on the right track. One thing I didn't see mentioned was string resonance and lid position.

I'll play with it a bit later tonight, but I bet playing with different mics (the ribbon mics likely to produce a similar sound will have "fig8" in the name), lowering (closing?) the lid, dropping hammer hardness, upping the sympathetic resonance, dropping the key noise, and as Qexl mentioned the note FX attack envelope. An EQ or two might help, maybe some reverb. I'll see if I can come up with something close-ish and share the FXP if anything nice comes of it.

Very nice.  I played this recently:

Journey HB D Classical

Here's how it sounds with your FXP (I took the lid off and set the celeste to 0.3):

Journey Spitfire Originals Intimate Knockoff

For good measure, here's how the same MIDI sounds with Intimate Grand:

Journey Intimate Grand

This might be a little closer. I decreased hammer noise in the higher registers, detuned it just a bit more, increased unison width, and added a little bit of the 200 Hz range back in.

Spitfire Originals Intimate Grand Knockoff 2

Spitfire Originals Intimate Grand Knockoff 2 - Audio Demo

I'd probably set max MIDI velocity to around 105ish, and Celeste Pedal around 0.3. Hard to say for sure without owning the Spitfire library to play myself, but I think it might be getting closer to the preset you used to record that audio above. Hope that helps!