frio

Looking at it again the OptiPNG export actually takes the mode you set it to only as a suggestion - setting it to grayscale when a paletted image is smaller produces a paletted image, setting it to RGB when grayscale is smaller makes a grayscale one, etc. For example a grayscale image with only 16 levels of gray will be smaller as a paletted 4-bit image (grayscale can only be 8 or 16 bits, so having 4 bits per pixel and a tiny palette header ends up being smaller in total). Turning off optimization in export won't help, then it just saves everything as 32-bit RGBA.
 
Looks like the online converter just does literally as told, removing color and saving as grayscale, so it's a safer bet.
Edit: if you want a local command program that can do the fix-up for you in bulk, ImageMagick has you covered. This command in Windows terminal/command prompt will make grayscaled copies of all PNGs in the current directory.
for %i in (*.png) do magick convert "%i" -colorspace gray "%~ni.gray.png" An in-place conversion is even simpler, but of course that overwrites the original files so be careful.
magick mogrify -colorspace gray *.png  
If you have a hex editor you can confirm the file type manually by looking at the outlined byte (red) in the IHDR chunk (chunk start green), if it's 00 or 04 it's grayscale.

Control-V doesn't paste a layer, it pastes a selected object which will merge automatically once you deselect it.
 
Paste a new layer with control-shift-V.

There's TR's Custom Palette Matcher if you want to reduce to a specific set of colors, instead of having the colors automatically determined. It's very simple to use: make the palette you want using the paint.net palette swatch, save it, and by default those palettes are shown in the plugin's list. If your palette doesn't take up all the slots though you'll have to duplicate one of the colors to fill all the rest.
 
There's also QuantDith, which supports dithering while lowering color count to a specific palette. It does support the same paint.net palette files but the plugin has a crash bug: you must edit the palette text files (click the "open palettes folder" on the palette swatch window to find them) and remove the 2 empty trailing lines manually that paint.net adds - else the plugin explodes on trying to load the custom palette.

Try Make Color Transparent from KrisVDM's pack. Choose black as the color to make transparent, 0.8 power, 0.0 full transparency threshold.
 

The reason you get dim colors from using an alpha mask is because the colors themselves are already "tainted" by the black background, and applying an alpha mask won't remove that blackness in them, which brings up an alternative solution: using Curves+ from pyrochild's plugin pack.
 
First grab the grayscale version of your picture to use for an alpha mask, then use Curves+ in HSV mode on the original. Uncheck "hue" and "saturation", and crank the only remaining curve (value) into a straight horizontal line at the top, i.e. you remove all value differences by maxing value out. Then apply the grayscale alpha mask on this value-removed image.

A couple options come to mind.
 
Easy but chaotic and not very configurable: Alpha to Dots
Less easy but configurable: extract the alpha mask, dither that with one of the several b/w dithering plugins, then replace the original alpha mask.
Alpha extraction: Alpha to Gray from BoltBait's plugin pack Dither: BoltBait's pack has Floyd-Steinberg dithering, Halftone dithering from Ed Harvey's pack, QuantDith can do several styles of dithering, including ordered ones. Reapply alpha: BoltBait's pack has Apply Alpha Mask. There's this other Alpha Mask if you want to paste the mask from clipboard.  
Top left: original, top right: alpha to dots, bottom left: halftone, bottom right: QuantDith.

How's something like this?

Plugins: Inner Shadow, Adjust Transparency from BoltBait's pack are the main ones.
Duplicate your object that's on a transparent background. Run inner shadow on the topmost copy. Uncheck "keep background" in the options. Run adjustments->transparency. Check "ignore transparent pixels" and go full opaque (+1). This gets you a hard inner shadow already, but it's very crispy and pixelated. If you don't want to use other plugins, you can work in a higher resolution and downscale afterwards, but what I used here is Erode to withdraw the shadow slightly, then AA's Assistant from dpy's pack to soften it.

AA's Assistant from dpy's plugin pack does preserve color data as far as I can tell.
Made an opaque red circle (255, 0, 0, 255) on transparent green background (0, 255, 0, 0) and after AA's assistant the opaque circle's edges have contracted and no green has bled into the red or vice versa.
 
There's also Alpha Blur from Tanel's pack that doesn't touch the other channels, only alpha, but it's a little more aggressive. Might contract the object too much in some cases without additional adjustment.
 

Assuming you have a separated, filled lineart figure (black lines, white fill, transparent surroundings) and you want the "plasma/flame" look, something like this might work:
1) Put figure on its own layer.
2) Duplicate figure layer.
3) Select topmost copy, set blend mode to multiply in layer properties. This will keep the lineart intact and on top of the colors.
4) Choose desired "plasma" colors in color palette. Effects->Render->Clouds, choose small scale, high-ish roughness.
5) Effects->Noise->Median, low radius (2-3), percentage 33 or so. Smothers the clouds.
6) Effects->Blurs->Surface blur. Further smothers the clouds.
7) Duplicate color layer. Select the bottom copy. Effects->Blurs->Zoom Blur, point it below the star, choose a length of your liking. Pushes the copy of the colors outside the figure.
8 ) Effects->Blurs->Gaussian blur to taste.
9)  Adjustments->Hue/Saturation, lower saturation and brightness to taste.

 

How about using multiple copies of the layer set to different blend modes? I often use that as a lazy non-destructive way of spicing up layers.
This is what you get if you duplicate the layer, set the bottom layer to normal blend 63/255 opacity, top layer overlay 255/255.
 

The Apply Alpha Mask plugin destroys color information (uses premultiplied alpha or something like that). It might be by design, but it it makes it unsuitable for purposes where that color information in transparent areas is important.
 
You can use this instead, it's a bit more rudimentary but despite the disclaimer on the page, works just fine in modern PdN and most importantly does not damage colors in transparent areas.
 
 

From the existing image you uploaded, the buttons are more or less pure black or white with varying states of transparency, instead of shades of gray with varying transparency, so best I can think of is just an approximation but not exact. The "Make color transparent" adjustment from KrisVDM's pack seems to do a reasonable job (set target color to 128, 128, 128, set power to 1). However since the insides of the buttons are close to the background gray, it would pretty much require more manual work than just a simple effect to get the transparency and color levels to match.