According to your preferred translation when does the fighting stop under what conditions?
From your link the prior verse
2:38
Say to the Unbelievers, if (now) they desist (from Unbelief), their past would be forgiven them; but if they persist, the punishment of those before them is already (a matter of warning for them).
2:39
39. And fight them on until there is no more tumult or oppression, and there prevail justice and faith in Allah altogether and everywhere; but if they cease, verily Allah doth see all that they do.
There are many translations
Verse 2:193
Yusuf Ali:
And fight them on until there is no more Tumult or oppression, and there prevail justice and faith in God; but if they cease, Let there be no hostility except to those who practise oppression.
Zohurul Hoque:
And fight them until there is no persecution, and religion is only for Allah. But if they desist, then let there be no hostilities except against the unjust.
T. J. Irving:
Fight them until there is no more subversion and [all] religion belongs to God. If they stop, let there be no [more] hostility except toward wrongdoers.
T.U. Hilali-M. Khan:
And fight them until there is no more Fitnah (disbelief and worshipping of others along with Allâh) and (all and every kind of) worship is for Allâh (Alone). But if they cease, let there be no transgression except against Az-Zâlimûn (the polytheists, and wrong-doers, etc.)
M. Pickthall:
And fight them until persecution is no more, and religion is for Allah. But if they desist, then let there be no hostility except against wrong-doers.
M.H. Shakir:
And fight with them until there is no persecution, and religion should be only for Allah, but if they desist, then there should be no hostility except against the oppressors.
2.193. And fight them until there is no more Fitnah (disbelief and worshipping of others along with Allâh) and (all and every kind of) worship is for Allâh (Alone). But if they cease, let there be no transgression except against Az-Zâlimûn (the polytheists, and wrong-doers, etc.)
In the Arabic the word is fitnah