How then could Pope Clement VIII issue this bull in 1604 changing the same Missal of St Pius V?
Did you read the Bull? He says through the years the missal had many errors due to printing or whatever, so he re-edited the corrupted missal so that is was put back to the original of Pope St. Pius V. He did not invent a new rite or change it.
From your link....."Although he very severely forbade under many penalties that anything should be added to it, or that anything for any reason be removed from it, nevertheless, in the course of time, it has come to pass that,
through the rashness and boldness of the printers, or of others, many errors have crept into the missals which have been produced in recent years....
...Having considered these innovations, in Our pastoral solicitude which induces us to earnestly
protect and preserve in everything and especially in the sacred rites of the Church the best and old norm, We have ordered in the first place that the above mentioned printed Missals, so corrupted, be banned and declared null and void and that their use be disallowed in the celebration of the Mass, unless they be entirely and in everything emended according to the original text published under Pius V...."
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