I have never seen a diode with a thermal pad on the anode.
Always on the cathode if one exists.
This is a Vishay SS2PH10 Schottky Barrier Rectifier used in my Buck LED driver in a DO-220AA package.
The cathode has a much larger pad for thermal dissipation.
And the temperature measurement point is the cathode.
A schottky is a metal-semiconductor junction, with the metal at the
anode. So it should be better for heatsinking
It may be true that the metal is going to conduct heat better but metal characteristics are not going to be affected much by heat.
The metal anode could be smaller than the cathode contact metal.
Source: Electronic Notes
The cathode also has a metal layer.
Source: Electronic Notes
Source: Electronics Maker
Which Method is Best?
Even though method 3 has the lowest RΦja method 1 may be the better method.
The RΦja listed is for leads only.
Method 1 would allow an additional thermal path from the case to the board.
Method 2 could be interesting if the vector pins were copper with large vertical fins.
Kind of like this: