First of all zakat is only paid for certain kinds of wealth like:
Money, financial income, silver and gold (also read islamqa #2795):
And those within whose wealth is a known right (70:24)
on fruits and grains (for details see islamqa #99843):
And He it is who causes gardens to grow, [both] trellised and untrellised, and palm trees and crops of different [kinds of] food and olives and pomegranates, similar and dissimilar. Eat of [each of] its fruit when it yields and give its due [zakah] on the day of its harvest. And be not excessive. Indeed, He does not like those who commit excess. (6:141)
on cattle (for details see islamqa #71267):
'By Allah, except Whom none has the right to be worshipped) whoever had camels or cows or sheep and did not pay their Zakat, those animals will be brought on the Day of Resurrection far bigger and fatter than before and they will tread him under their hooves, and will butt him with their horns, and (those animals will come in circle): When the last does its turn, the first will start again, and this punishment will go on till Allah has finished the judgments amongst the people." (sahih al-Bukhari)
I hope I didn't miss anything.
Note that we don't exactly know what of these kinds will be in Jannah, but we know that we will be given them and this without any due (tribute). So Zakat is excluded for those (believers) who have been doing good in this life and entered Jannah as is clearly mentioned in the Qur'an:
Whoever does an evil deed will not be recompensed except by the like thereof; but whoever does righteousness, whether male or female, while he is a believer - those will enter Paradise, being given provision therein without account. (40:40)
'Isa and zakat
This will apply to any of them no matter if it is 'Isa () or anybody else.
Note that you assume that 'Isa is alive this actually is a discussed matter some scholars say that he died (not by the hands of the Jews or his pursuers) and was raised to Allah, whether he is in Jannah or not is not mentioned in the Qur'an, nor is indicated in the qur'an whether he is actually alive or not. Some ahadith indicate that when he will be resurrected he won't die a second time.
Read for exampple on Surat Al `Imran 3/55 about the death of Jesus(puh)?
So based on the above your Qur'an-quote:
...so long as I remain alive,
applies for 'Isa's lifetime where he is/was/will (be) able to spent or pay zakat, which is in this life only. This is the interpretation of zakat as a kind of financial tribute.
But in Arabic zakat also may mean a (inner) purification (for example by leaving sins and doing good deeds) that's also how the (financial) zakat was presented in the Qur'an (as a purification):
Take, [O, Muhammad], from their wealth a charity by which you purify them and cause them increase, and invoke [ Allah 's blessings] upon them. Indeed, your invocations are reassurance for them. And Allah is Hearing and Knowing. (9:103)