I have an inexpensive AquaSource toilet that's about two years old that will not hold it's water level in the toilet bowl. I just did a test: flushed toilet, marked water level in toilet bowl with pencil, and observed water. Within seconds after the water shut off the level started dropping. It dropped about 1/2". Why? It needs the extra water for a good flush. What needs to be done so it doesn't drain out this water?
Plumbing – Why Does Water in Toilet Bowl Drop
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The overflow tube drains directly into the bowl, not the tank. The only way I can think that it would prevent the tank from filling is if it was cracked or had a hole in it and allowed tank water to drain into the bowl. If this was the case, you would notice the fill valve cycling if it was a slow leak or never shutting off if it were a large leak. The reason the tank fills quickly when you divert the bowl refill tube into the tank is that you are simply not splitting the water from the fill value between the tank and bowl any more.
It sounds like your fill valve assembly is the problem. The fill value has 2 outlets, one that directs into the tank, and the other that sends water into your bowl refill tube. My best guess is that something inside of the fill value got clogged with sediment, hard water deposits, or something else that restricted it. These are relatively cheap to replace and likely not worth the time to clean them out in my opinion.
More than likely the tank is filling the bowl above the bowl's fill level, and the bowl drains slowly until it's level with the top of the trap (or siphon).
Unless it's completely draining, there's really nothing to worry about.
Best Answer
Assuming that the water does not continue to drain after it reaches the half-inch drop, I believe that what you're seeing is by design (intentional or otherwise). When the tank on the toilet refills, a small portion of that water goes to the toilet bowl to refill it. The bowl is typically overfilled to ensure the water level fills up to the edge of the siphon (I'm going to refer to it as such, even though this is not the name on many newer toilets) to prevent sewer gas leakage, and the excess drains over the edge. I suspect that your toilet is of such a design that the water level inside the siphon equalizes slower than one would expect.
There are a number of reasons that the water level could equalize more slowly; some models create a back-pressure inside the siphon, some create a positive air pocket for additional suction during the flush, or it could just be the intentional design of the siphon.
I doubt it is something to worry about.