My quick 10 minute search online reveals that the Honda GX390T2 engines are sold out.pI have to agree with @WrenchIt . let it sit for several days with the penetrating oil and see if you can move it. However if it is the main bearing the oil is not gonna help. Almost every engine i have unseized was never really the same afterwards. They smoked or had other issues.
If the engine seized quickly maybe the cylinder is not that scored and you could rebuild it. depends if the journal on the crank is scored. I am rebuilding an older gx240 right now. Got the rebuild kit from Everest Parts LLC for about $65 that includes gaskets, piston, rings , etc. It's just a fun thing for me to do since gx240's are very cheap in the first place.
A guy brought a seized 928 to me. same reason. very little oil in crankcase. I had a spare gx270 in the shed . Charged him $150 for engine and $100 to switch them out. He was happy as a clam.
In your case , unless you are extremely lucky , you may have to change engines. Right now there are not too many cheap HSS machines out there that you could scavenge for an engine. For $900-1300 for a new engine , plus labor , I just don't know what I'd do. I do like the older HS models better. An older 1132-1332 can be had for around 1200-1500USD in the summer. A lot more now.
If you were close to me I would love to help out. I love challenges like this. Many people have brought me seized engines and I love bringing them back to life. It's 50-50 at best though on success (or less )
Unfortunately I called the nearest Honda Power Equipment dealer in Connecticut and he was only willing to assert that he's available next Monday on Columbus Day after 8am and informed me that Service and Parts will get involved in expediting a query ONLY to a source a complete GX390T2 engine during business hours. This was at 3:59PM EST before they closed at 4PM. At least I got their attention. I see where you're going with this and I'm interested with a short block as I have shade tree experience in swapping parts. Shop manual makes is look way too easy. Removal of negative battery cable, wire harnesses on electric start models, air cleaner cover, silencer nose, recoil starter and auger belts. THEN the fun begins with 4 hold down bolts for engine removal. From there I have 2-3 months before I see snowflakes.Is a short block available from Honda ?