This train of logic doesn't make any sense.

    the primary goal of the government should be preventing foreign powers,
    potentially hostile ones, from getting access to the secrets he possesses.

    Publicly threatening to arrest and try him for serious and potentially
    capital offenses like espionage while he is in territory not subject to
    the US or any close ally that would be likely inclined to cooperate given
    the circumstances is, from that perspective, quite foolish.

If the government were to take that tack, it would only encourage leakers and 'spies' to grab the most valuable documents possible, in essence blackmailing their way out of prosecution.

If you're the US government, your default assumption must be that Putin has a hard drive with everything that Snowden took. If that's the case, it makes absolute sense to publicly threaten to arrest him and charge him with the most severe of consequences.

Look at it from a game theory perspective; the US government 'lost' the first game to Snowden. The only reason they are still engaging with him is that the US is playing a repeating game. They need to make the penalty for leaking high enough to persuade other potential leakers to stay quiet.