You can use the brush strength for this :
setting it to a value lower than 1
will output the result you're looking for.
Blender's painting system works like a physical painting system, you know those in which you use a paper canvas and gouache-like paints. You don't choose a red gouache with 0.5 opacity, you chose a regular red gouache and the strength and pressure you use when you paint decide how opaque the stroke will be.
Most painting softwares work the same way, in G.I.M.P. for example, when you chose a color for the background or the foreground, they only allow you to pick RGB, LCH or HSV and no alpha, in Photoshop, it's the same thing :
As far as I know, it works the same way everywhere : you pick a color and you set the strength of the brush (or the opacity of the brush in some softwares) to a value you like if you don't want a perfectly opaque stroke.
In Blender, you can resize the brush with F and change its strength with SHIFT + F. This is the result I had when using a brush with 0.5
, 0.066
and 1
strength value :
You can see that the exported image will actually have alpha.