Amber Varnish and Medium

I am aware of three other suppliers of what appears to be genuine Baltic amber dissolved into a drying oil with and without a solvent. Put amber painting medium into Google and you should find them within a few pages. None are cheap, but these others are less than the brand you mention.
This sidesteps the idea of whether such a medium is actually historical and if it is beneficial. As to the historical use of such mediums. There are 17th century recipes that mention amber as an ingredient. There is some question as to whether they are actually referring to what we call true amber today. Many believe that a number of resins were called amber at the time. Even the term varnish is related to bernice which is a synonym for amber.  This could suggest that almost any resin cooked into an oil could be called amber varnish or it could suggest a more wide use of true amber containing varnish/mediums. It is certainly true that resins cooked into hot drying oils (linseed, walnut) was the most common form of varnish until at least the 16th century. There an almost mythical respect for the idea of amber varnish in the luthier field, but others poo poo the idea. As to detecting amber in oil paintings, I only know of one study where the Getty found amber markers in paint samples from a work by Orazio Gentileschi.
To make a hard resin (meaning a resin that is not soluble in any solvent and is only soluble in very hot oil) into an oil varnish you need to heat the resin to a very high temperature as well as heating the oil to close to its flash point. This drives off organic components of the amber and brigs its solubility closer to that of the oil. Thinning with a solvent can only be accomplished after the union of the resin and oil and when the solution has cooled to the point where it would not immediately burst into flame.
This is a very dangerous operation and should not be done outside of a laboratory or by an experienced operator in a manufacturing facility equipped with full safety equipment. The end product is quite dark and will lower the value and tone of whites and blue colors. It should also be mentioned that the resiliency of the amber is very much altered by the thermal processing and it should not be thought that somehow a dried amber varnish is as impermeable as the source amber.  In fact, even amber is far more sensitive to the environment than most believe. Baltic amber has survived millions of years but generally has done so in the absence of oxygen. Witness the deterioration of the Amber room in the Hermitage because the amber is exposed to the environment.
However, there is one real benefit to the use of hard resin/oil varnishes over mediums that contain soft resins. When added to oil paint they create paint films that are less sensitive to the solvents that are used to remove old surface varnishes in future conservation treatments. They also contribute a particular drag under the brush and set quickly, allowing for early blending.  I do not believe that amber varnish offers anything above a true hard copal (like Congo copal or Zanzibar copal) varnish. Even this is moot as high quality hard copal mediums and varnishes are as difficult to find as amber mediums/varnishes.
There are certainly negatives to these hard resin oil mediums as well. These varnishes will darken your paint over time if overused (more than a drop or two added a “blob” of paint. They also contribute brittleness unless the oil component is quite high or the medium is added in only very small amounts. I do not believe claims of them adding flexibility. Show me a study that proves this.
Full disclosure, when I was more of a practicing painter, I did like to use judicious additions of Congo copal medium to my paint (mixed with a bit of stand oil to counteract brittleness) when I was searching for a particular effect (super fine lines, or to allow for minute and sophisticated blending). I have seen a small degree of lowering of tone in some of my works, certainly not all where I used such a medium, but probably those where I added a bit more than I should have. However, these few examples prove nothing about future longevity as this period of time (15-20 years) is nowhere long enough to predict the long-term preservation.
So finally, if you are willing to spend a premium and add only very small amounts of a true amber medium to your paint to achieve a particular effect, go ahead. However, alkyd mediums allow for increased transparency, richness, and can accelerate the dry time of oil paint without contributing solvent sensitivity (like soft resins) nor serious brittleness (like all natural resins, when used in large proportions).