Do catalysts really not participate in chemical reactions? So why can the reaction rate be changed?

Does catalyst really not participate in chemical reactions? So why can the reaction rate be changed? IUPAC defines a catalyst as follows: a catalyst is a substance that changes the reaction rate but does not change the total standard Gibbs free energy of the reaction. This effect is called catalysis, and reactions involving catalysts are called catalytic reactions.
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The catalyst itself may not necessarily be added, and the quality may not remain the same (some become more, some less).
For example, permanganic acid oxidizes oxalic acid, and the product divalent manganese is the catalyst (and more and more, trivalent manganese and tetravalent manganese are also used)
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(Of course, this reaction will be very slow when divalent manganese is not added at the beginning. After all, it is not easy to carry out oxidation and reduction between the two anions. Of course, stir quickly with your hands for half an hour. It still responds after an hour)
Of course, the mass of the catalyst decreases after the reaction
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Sodium consumption is very small, so it is still used as a catalyst.
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