GGale has the colour adjustment sliders always visible so there is minimal burden to tweak colour values. Aseprite allows you to leave the palette editor open while you work, but you have to reopen it every time you launch the program and in a (usually somewhat broken) floating window too. Also no HSL.

You can also leave the foreground color open (have to click and drag a bit to set it to a pinned state). This allows you to adjust the color without changing the palette color itself. But yes, most of the same caveats.
Is there any way to swap/replaces colour in the palette with a single drag+modifier like in GGale?
You can replace with the copy, paste hotkey in place of the drag. So you can unhide the things in
ptoing's robot picture.
And... hah. While I just figured out a cute way to swap single colors, it's not as good as GG's for sure.

It'd be alright if you could set reverse colors to a hotkey, but you can't right now.

So short answer, no, longer: I think replace is comparable as far as speed, "swap" is not.
For merging colours multiselect then merge-as-average or merge-as-first/last would be a nice feature that is lacking in all pixel editors AFAIK.
Ah. Yeah, that's a good idea. There's a thing like that for gradients in a lot of stuff, so this type of merge doesn't seem too out of the question.
I don't like starting software through steam,
Then it's a good thing you don't need to! Aseprite is DRM free, so you can just double click the exe and steam won't launch. I have a shortcut to it.
Could it work that you have a complete frame overview somewhere?
You appear to be out of luck there, for now.
Could I set myself what kind of bg I want for transparant?
Yup.

Why is the checkerboard surface larger than the actual image? If I set the zoom even higher the checkerboard space grows yet the image doesn't!
If I'm understanding correctly, that's fixed with Apply Zoom?
Merge colors, I actually meant merge indexes. For example I might have 2 sprites from different sources in my canvas and I want them both to use the same palette. I'd like to drag the new colors onto the old colors (which is already possible with the copy function)
Does this gif look like it'd do what you want?

Select the new colors, press control+C (Copy), select the first old color, press control+V (Paste).
If you truly want to get rid of the old colors, you can use control+X (cut) instead of control+c(copy)
Am I understanding correctly?
As for color picking, I'd love to have the "palette editor" on screen all the time.
You are free to have it open all the time, but I know it's not as good a solution as what you really want. I think someone made an issue for this, but I looked and could not find it.
Really nifty in GraphicsGale is its load palette function. In their interface you can manually remap your sprite, or copy only specific colors, or leave specific old colors intact, when you import another color.
That is indeed a really nifty interface. There's nothing comparable in Aseprite that I'm aware of. You can copy and paste palette colors from different tabs a bit like described above, but that doesn't even let you see both palettes at once.
Thanks so much for developing this tool,
I uh... didn't! I'm just a groupie. I have read most of the commits from the past few years which is why I know so many silly obscure things. But nope, I'm not dacap.
Another thing that has bothered me a lot in Aseprite when editing tilesets, is that I can't snap selections to a grid! I can make perfect 32x32 selections, but then moving my tile over the canvas I have to place it perfectly manually.. :/
I recall some weirdness as far as drawing with snap to grid, to fix something someone else didn't like, heh.
But doesn't drag+alt do what you want as far as moving tiles? (Note, alt opens the color picker by default, so it really does have to be drag
then alt.

Edit: Oh yeah, if you double click a tile with the select tool active, Aseprite will select that tile. It seems like you know this since you said you could easily make tile selection, but just in case. You can do both of the above things without snap to grid even being enabled.
It wasn't specifically asked, but that question reminded me of my favorite "hidden" Aseprite feature. Spacebar lets you move some operations before you commit them.

If you start the line tool, of the rectangle tool, or the rectangle select tool etc in the wrong place, you can just hold space bar and move it. Don't need to click again to start a new operation.
Okay, probably done editing.