The sentence is possibly incorrect and fooled you. It probably should have used la composant, although we would need more context to be sure. With a feminine or a plural, you probably wouldn’t have confused the pronoun/verb le/la/les composant (composing it, it being the preparation) with the article/noun le composant (the component):

…chaque prestation la composant fait l’objet…

…each benefit composing it (i.e. composing the preparation) makes…

In itself this sentence is not correct ; the pronoun « le » is masculine singular and there is no word in it that is masculine singular and that could be referred to by this pronoun, not « préparation », not « paiements » ; therefore, either the pronoun is erroneous and most likely it is « les », or there is something else that is being mentioned before this sentence and that is what the pronoun refers to. In case this latter possibility is not verifiable, then, most likely what is being referred to is « paiements », which is why I supposed above that « les » was the pronoun needed. (Les paiements sont composés de prestations.)

• Une fois la préparation des paiements terminée, chaque prestation les composant fait l’objet d’une mise à jour de ses données au dépôt Rentes.

In other words, this sentence is equivalent to the following.

• Une fois la préparation des paiements terminée, chaque prestation composant les paiements fait l’objet d’une mise à jour de ses données au dépôt Rentes.

Your second sentence is not correct.

The sentence is something like a latin absolute ablative. An equivalent form could be: une fois que la présentation des paiements est terminée, …

https://fr.wikipedia.org/wiki/Ablatif_absolu?wprov=sfti1

I also think that the correct pronoun is “les” and not “le”