There is no contradiction here. I recommend you read tafsirs (commentaries) on how this ayah is interpreted and any other ayahs you have questions about.
Many scholars consider ayah 5:3 to be the last ayah revealed in the Quran and that no other ayah came after it.
According to Tafsir Ibn Kathir, Quran 5:3 says that his "favor" is the completion of Islam and since it is complete, no other religion is needed.
(This day, I have perfected your religion for you, completed My favor upon you, and have chosen for you Islam as your religion.) This, indeed, is the biggest favor from Allah to this Ummah, for He has completed their religion for them, and they, thus, do not need any other religion or any other Prophet except Muhammad. This is why Allah made Muhammad the Final Prophet and sent him to all humans and Jinn. Therefore, the permissible is what he allows, the impermissible is what he prohibits, the Law is what he legislates and everything that he conveys is true and authentic and does not contain lies or contradictions.
According to the Study Quran (p. 650) on Quran 5:3, the completion of his "favor" refers widely to two views, the establishment of the rites and procedures for Hajj, or the completion of the Quran.
The “perfection” of the religion and the
“completion” of blessing are widely understood as referring either to the fact that the Prophet’s pilgrimage to Makkah established the rites and procedures for the final Muslim ritual obligation, the ḥajj, or to the completion of the Quranic revelation, although not all agree that this was the last verse to be revealed.
Some claim that no other ritual or legal rulings were revealed to the Prophet after
this day (Ṭ, Ṭū, Z), although others assert that additional verses containing legal,
but not ritual, prescriptions were revealed after this verse (Q).
According to Tafsir Al-Jalalayn, the completion of his "favor" refers to perfecting the religion of Islam and by giving the Muslims at the time of Prophet Muhammad (SAW) safe entry into Mecca.
[5:3] Forbidden to you is carrion, that is, the consumption of it, and blood, that is, what has been spilt, as mentioned in [sūrat] al-Anʿām [Q. 6:145], and the flesh of swine, and what has been hallowed to other than God, in that it was sacrificed in the name of something other than Him, and the beast strangled, to
death, and the beast beaten down, to death, and the beast fallen, from a height to its death, and the beast
gored, to death by another, and what beasts of prey have devoured, of such animals — except for what
you have sacrificed duly, catching it while it still breathes life and then sacrificing it — and what has
been sacrificed in, the name of, idols (nuṣub is the plural of nuṣāb) and that you apportion, that is, that
you demand an oath or a ruling, through the divining of arrows (azlām: the plural of zalam or zulam,
which is a qidḥ, ‘a small arrow’, without feathers or a head). There were seven of these [arrows], [marked]
with flags, and they were retained by the keeper of the Kaʿba. They would use them for abitrations and
when they commanded them they obeyed, and if they prohibited them they would desist; that is wickedness, a rebellion against obedience. And on the Day of ʿArafa in the year of the Farewell Pilgrimage, the
following was revealed: Today the disbelievers have despaired of your religion, of you apostatising from
it, having hoped for it [earlier], for now they perceived its strength; therefore do not fear them, but fear
Me. Today I have perfected your religion for you, that is, its rulings and obligations (after this [verse]
nothing about [what is] lawful or unlawful was revealed) and I have completed My favour upon you,
by perfecting it [your religion], but it is also said by [effecting] their safe entry into Mecca; and I have
approved, chosen, Islam for you as religion. But whoever is constrained by emptiness, by hunger, to
consume some of what has been forbidden him and consumes it, not inclining purposely to sin, to an act
of disobedience — then God is Forgiving, to him for what he has consumed, Merciful, to him by permitting it to him, in contrast to the one who [purposely] inclines to sin, that is, the one actively engaged in
it, such as a waylayer or a criminal, for whom [such] consumption is forbidden.
You can check out more tafsirs regarding Quran 5:3 here.
All Muslims alive during the revelation of this ayah to us living in the present day are benefiting from Allah's "favor" upon us which is the perfection/completion of Islam.
And according to some views/tafsirs, the "favor" also relates to the safe entry of Muslims into Mecca as well.