First, I agree with the above comments: I use a 400 fine-grit sandpaper to clean off the existing thermocouple tip and I clean off the pilot tip as well.
As a separate precaution, I would check the spark on the igniter assembly by disconnecting it then watching for the small blue spark at the hand-button (DUH, only after turning off the gas!)
Yes, you can use the Honeywell 30mV t-couple with the State if/when the threads in the gas control valve seat fit.
Lastly, note that some State water heaters have a high-temperature shunt soldered in-line with the thermocouple. These are a retrofit part to repair problems in hot-weather climates (like Arizona and Southern Nevada.) In that case, the thermocouple with the shunt 'ignores' high ambient temperatures in garages, etc. I have had to replace my State water-heater thermocouple a few times because the shunt resistor cracks. Of course the cracking problem only occurs in cold, winter temperatures.
The parts list for your heater is found here; and it looks like yours (at least originally) did not have the high-temp shunt resistor version of the thermocouple. Your thermocouple #9000056015 is manufactured by AO Smith and (for example) could be purchased here or elsewhere.
Bottom line: go get the Honeywell and a 2nd push-button igniter; order a 2nd AO Smith thermocouple online; clean and test your existing ones if you are up for it....please post back your progress.
I have used a product made by permatex called ultra copper it is RTV for use at high temps. It works well to seal and create a conductive surface The RTV seals and the threads still make contact. Ultra copper in the copper colored tube. It only takes a little to do the job and a well sealed tube stored in a fridge last a very long time.
Best Answer
There are only a few types of anodes out there -- different materials (aluminum, magnesium, aluminum/zinc) and different form factors (rigid vs flexible/segmented, hex head vs combination).
Your heater comes stock with an aluminum hex anode (all American/Whirlpool/US Craftmaster heaters use aluminum, and the manual for your heater has a parts diagram on page 30 that depicts a hex anode -- so you should be able to replace it with a standard hex anode, unless you have overhead clearance problems that require a flexible unit. I'd get a magnesium anode for your replacement if at all possible -- our bodies don't get along particularly well with aluminum ions.