Which surface finish for edge connector plating to increase number of mating cycles with sliding spring contact?
The goal of plating is to protect copper or other metals from oxidation (which increases contact resistance). Since gold doesn't oxidize contacting surfaces need a sufficient amount. I can tell you from personal experience that a gold flash &lt;1um doesn't do much.
Here is some info from a manufacturer:

KAT Electroless Nickel/ Immersion Gold (ENIG)
KAT ENIG is the industry standard for producing uniform mid-phos EN deposits with a thin topcoat of immersion gold, over copper substrates. This PCB finish is highly resistant to corrosion, and is both solderable and aluminum wire bondable. It is an ideal contacting surface.
Electroless Nickel, Electroless Palladium, Immersion Gold (ENEPIG)
ENEPIG is formed by the deposition of electroless nickel, followed by
electroless palladium, with an immersion gold flash.  ENEPIG has
exceptionally wide application: it is suitable for soldering, gold
wire bonding, aluminum wire bonding, and contact resistance.
KAT UF (ENEPIG) Universal Finish
This unique Ni/Pd/Au surface finish is solderable, aluminum and gold wire bondable, and a superb contact surface. The recommended thickness is 3 – 5 microns (120 – 200 µins) of electroless nickel, 0.16 micron (4 – 6 µins) of electroless palladium, and 0.02 to 0.04 micron (1 – 2 µins) of immersion gold.

The thicker the gold the better, how long will it last? There isn't much information on that. From Viasystems surface finishes

If your really worried about it and this is essential for your product, I think I'd do some mechanical testing while measuring the contact resistance (Here as an example) Otherwise, stay away from the really thin flashes and the thicker the better. Remember that thicknesses and some definitions vary from manufacturer to manufacturer (such as the definition of hard and soft gold) so make sure you know what your getting.
From this article on contact resistance:


Golden Rule No.3: Gold Coatings Can Be Used For High Durability

Coating a contact with pure (i.e. soft) gold generally results in a connector
with low durability and high insertion forces (i.e., high coefficient of friction),
especially when the thickness is greater than 0.13 microns (5 microinches).
In practice, gold coatings are usually hardened by adding small amounts
cobalt or nickel to the gold. Such coatings are defined as ‘hard gold’ and
produce coatings with a low coefficient of friction and excellent durability
characteristics. Hard gold coated contacts can generally withstand hundreds
to thousands of durability cycles without failing.
The durability of hard gold coatings can be enhanced by using an underlayer
having a hardness value that is greater than that of gold and which will
provide mechanical support. Nickel is generally recommended as an
underlayer for this purpose. Lubricants are also effective at increasing the
durability of gold coatings. Generally, lubrication can increase the durability
of a gold contact by an order of magnitude.