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While it is problematic on deciding if there is a legal authority to search or not, and whether you may resist it or not, the line for when you can resist a detention is much clearer. Note that the laws specifically allowing a person to detain you for investigation have been posted, and two different laws allowing the arrest have also been posted (citizen's arrest and prevent the consequences of a theft).

So, your resistance becomes a crime when you leave the scene. Specifically, Penal Code section 38.06 says:

ESCAPE. (a) A person commits an offense if the person escapes from custody when the person is:
(1) under arrest for, lawfully detained for, charged with, or convicted of an offense;

Note that it does not say arrested or detained by a peace officer. The punishments later in that section make it more explicit by having special circumstances for being in a law enforcement facility. It also makes it a first degree felony if you use a deadly weapon to escape.

On the search side, please note that Code of Criminal Procedure Article 18.16 does say the person has to seize the stolen property, and then the person only if they can be taken. To seize property certainly implies to me the search is authorized under those circumstances. It also implies the LPO better be correct though.