Answer: In the name of Allah, Most Compassionate, Most Merciful,
Assalam’aleykum, I pray this finds you in the best of states.
Jazakum Allah khayr for your question!
The only prayers you have to pray without fail are the obligatory prayers (Witr included) and the emphasized sunna prayers of the day you are in along with the missed obligatory prayers. This is what you have to pray, not the missed sunna prayers.
Please see the link below that explains what the emphasized sunna prayers are:
The position of all four schools of Sunni law is that it is obligatory (fard) to make up all missed obligatory prayers, regardless of why they were missed. And prayer is the first thing we will be questioned about on the Day of Judgement, as the Prophet (Allah bless him and give him peace) informed us.
As for Witr, then it is necessary (wajib) because of the many hadiths emphasizing it. The Messenger of Allah (peace and blessings be upon him) said, “Witr is a duty, and whoever refuses to perform it isn’t of us” (Abu Dawud and Ahmad). However, because it is a less emphatic duty than the obligatory prayers, you can first make up your obligatory prayers, and make up your witr prayers after. However, both must be made up nonetheless. According to the Hanafi school, one would still have to stick to one’s confirmed sunna prayers (sunna mu’akkadas), because they remain strongly enjoined such that missing them even once without excuse is blameworthy, and making this a habit is sinful [Ibn Abidin, Hashiya].
As for the sunna prayers, there is no make up for them.
There is one exception: the sunna prayer that should be performed before the obligatory Fajr prayer. Performing it after its time is called “qada” (makeup). This happens when the Fajr prayer of the day has been missed along with the sunna prayer of Fajr. If you miss the Fajr prayer but make it up before Zuhr during the same day, you would perform the sunna prayer too. Otherwise, and if you are making it up at any other time, you do not pray the sunna prayer with it [Ibn `Abidin, Radd al-Muhtar `ala al-Durr al-Mukhtar; Tahtawi, Hashiya on Maraqi Al Falah].
However, it is a general sunna to perform an equivalent amount of voluntary sunnas to “make up for” the lost reward of recently missed sunnas.
And Allah knows best.
I hope that the above answers your question. If something is unclear please don’t hesitate to ask again.
May Allah Most High grant you the best of this world and the next. Please keep us in your du’as!
[Ustadh] Sufyan Qufi