Sand based tank

Stir the sand up real good, do a massive water change. Repeat that twice. That will dramatically reduce the silt in the water, give it another day or two and it will be clear.

Also the plants alone won't provide much bacteria to colonize the sand, you would be better off taking a little bit of gravel or a small amount of filter material from the other tank to put into the 10gal once you add the betta, don't do it before hand.
 
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