Learn French: Le vétérinaire a posé la puce et a vacciné l'animal. - The vet inserted the microchip and vaccinated the animal.

In French, the verb poser (to put or place) is commonly used for medical or technical installations. This includes microchips, braces (poser un appareil dentaire), or even applying a bandage. While you could technically use implanter, poser is the most natural everyday choice here.

Doesn't puce mean flea?

Yes, puce literally means flea, but it is also the standard French word for a microchip or computer chip (short for une puce électronique). In this context, poser la puce means to microchip the pet, not to infest it!

This lesson is about sentence-initial Que + Subjunctive. How could I turn this sentence into that structure to express that I am glad about the vet's actions?

You can frame the whole event as a subject clause by adding Que at the start and putting the verbs in the past subjunctive. For example: Que le vétérinaire ait posé la puce et ait vacciné l'animal est une bonne chose. (That the vet inserted the microchip and vaccinated the animal is a good thing).

Why is the auxiliary a repeated in a posé and a vacciné? Could I just say a posé la puce et vacciné?

In French, it is much more common and natural to repeat the auxiliary verb (avoir or être) after a conjunction like et, even when the subject is the same. Dropping the second auxiliary is sometimes done in formal literary writing, but in everyday speech and B2-level writing, you should repeat it.