I don’t know what colour changes you are after, but if you look at a couple of other brands, you will find they don’t need a primer / bridge coat . Mylands eggshell will stick straight to a well prepared pre-painted surface, and is a good drop of paint for this scenario. A favourite for @rontaylor .
If you want a water based “self undercoating” gloss, Helmi is the same spec as Mylands.
Mythic black label eggshell is a self priming acrylic. It needs help with a conditioner, (I think, it is a bit stringy). Also, it is not as tough as “eggshell” so you could look at the Mythic semi gloss sheen.
Your more conventional spec with undercoat and Colortrend topcoats: for straight undercoating, Mythic Primer is very white, and quick drying and good adhesion and applies very well, so I would pick that over Coverstain on a pre-painted surface. The advantage of Coverstain is the extra body, but it is not needed here, I would think.
If there is any staining, make sure the second coat of Mythic has 4 hours to dry and lock in the stain before applying the second coat.
Re my thinking with thin Mythic primer., a few years ago now, it seemed that most professional UK painters were moaning that acrylic paint has no body, and it was hopeless compared to old heavy body oil paint systems which cover and fill imperfections to a certain degree i.e. old oil paint helps cover a multitude of sins.
I looked at it back to front, (how wrong can the rest of the world outside the UK using acrylic be!) and instead of ignoring all the benefits of acrylic, and trashing it for being thin, why bnot play to its strengths. So I made sure the preparation and filling was immaculate (which is relatively easy with the right dust extraction tools and abrasives). i.e. I accepted that the acrylic paint was too thin to help with filling out the surface, but over a well prepared base all it had to do was stick and add colour.
That worked - (full details here) and that is the thinking here. With good sanding, you will have the smooth base, and if the “thin” undercoat has covered well, then the topcoats will fly on and do their job, whether they are too thin or not.