Describe the solution you'd like
I want the alpha to be included in updating the health frame's color.

Describe alternatives you've considered
I guess I could forego oUF, or maybe hook into the function (no clue if this is possible).

I wanted to make my own branch and pull requests, but I lack the rights. The solution should be as simple as changing the function to:

local function UpdateColor(self, event, unit)
	if(not unit or self.unit ~= unit) then return end
	local element = self.Health

	local r, g, b, color
	local _, _, _, a = self.Health:GetStatusBarColor()
	if(element.colorDisconnected and not UnitIsConnected(unit)) then
		color = self.colors.disconnected
	elseif(element.colorTapping and not UnitPlayerControlled(unit) and UnitIsTapDenied(unit)) then
		color = self.colors.tapped
	elseif(element.colorThreat and not UnitPlayerControlled(unit) and UnitThreatSituation('player', unit)) then
		color =  self.colors.threat[UnitThreatSituation('player', unit)]
	elseif(element.colorClass and UnitIsPlayer(unit))
		or (element.colorClassNPC and not UnitIsPlayer(unit))
		or (element.colorClassPet and UnitPlayerControlled(unit) and not UnitIsPlayer(unit)) then
		local _, class = UnitClass(unit)
		color = self.colors.class[class]
	elseif(element.colorSelection and unitSelectionType(unit, element.considerSelectionInCombatHostile)) then
		color = self.colors.selection[unitSelectionType(unit, element.considerSelectionInCombatHostile)]
	elseif(element.colorReaction and UnitReaction(unit, 'player')) then
		color = self.colors.reaction[UnitReaction(unit, 'player')]
	elseif(element.colorSmooth) then
		r, g, b = self:ColorGradient(element.cur or 1, element.max or 1, unpack(element.smoothGradient or self.colors.smooth))
	elseif(element.colorHealth) then
		color = self.colors.health
	end

	if(color) then
		r, g, b = color[1], color[2], color[3]
	end

	if(b) then
		element:SetStatusBarColor(r, g, b, a)

		local bg = element.bg
		if(bg) then
			local mu = bg.multiplier or 1
			bg:SetVertexColor(r * mu, g * mu, b * mu)
		end
	end

	--[[ Callback: Health:PostUpdateColor(unit, r, g, b)
	Called after the element color has been updated.

	* self - the Health element
	* unit - the unit for which the update has been triggered (string)
	* r    - the red component of the used color (number)[0-1]
	* g    - the green component of the used color (number)[0-1]
	* b    - the blue component of the used color (number)[0-1]
	--]]
	if(element.PostUpdateColor) then
		element:PostUpdateColor(unit, r, g, b)
	end
end

You could try self.Health:GetStatusBarTexture():SetAlpha(0.5) instead, as :GetStatusBarTexture() returns the Texture object and not the texture file (that'd be :GetStatusBarTexture():GetTexture()).

I wanted to make my own branch and pull requests, but I lack the rights.

If you wanted to do this you'd fork the project, create your branch with your changes, then submit a pull request to the originating project from your modified branch, there are GitHub help articles about this subject. But please see if my suggestion works first.

My problem with that is then the UpdateColor function overrides the color for a short moment making the frame blink at full alpha causing a look like this:

Totally agree with this, I have a similar situation.
UpdateColor should contain the alpha value, so we don't have to modify the oUF code directly, or write a bunch of extra code in our own layout.

How exactly did you get that blinking?

Using this I experienced no blinking whatsoever:

local Health = CreateFrame('Frame', nil, self)
Health:SetAllPoints()
Health.colorClass = true
Health.PostUpdateColor = function()
    Health:GetStatusBarTexture():SetAlpha(0.5)
end
self.Health = Health

How exactly did you get that blinking?

For context, I'm working on an extension of the Fader/range indicator feature in the ElvUI unitframes which uses oUF. Currently, it is only possible to alter the alpha of the entire unitframe by changing the alpha of the Health frame, I believe, however, I wanted to only lower the alpha of the "foreground," achieving the look of the gif in the previous comment.

I am new to Lua and any wow addon development, but it seemed that changes were required to oUF and oUF_Fader.
In oUF_Fader I changed the ToggleAlpha function from setting alpha like this: self:SetAlpha(endAlpha).
To:
local r, g, b, a = self.Health:GetStatusBarColor()
self.Health:SetStatusBarColor(r, g, b, endAlpha)

Is there an oUF discord that is better suited for questions?

You'll need to ask the ElvUI people about this, as the solution I provided works fine for oUF, but you're using a fork of it with a plugin we have no control over, which seems to not have any options for overriding.

Altering the alpha of the statusbar texture object should work in both cases though, so you could replace :SetAlpha(endAlpha) with :GetStatusBarTexture():SetAlpha(endAlpha) in the fader plugin too, but we provide no guarantee it'll work since it's not our code.