The article used in 58:13 is "فإذ" which would translate to "so when" and is followed by past-tense verbs (the first verb "تفعلوا" is present-tense, but is negated by the past-tense article "لم" so it describes something in the past). This is not a conditional sentence, so the use of past tense means the past (rather than a generic tense that covers the present and future like the case of a conditional "إذا" for example).
There is only one other use of "فإذ" in the Quran ("إذ" by itself is used a lot),
and this verse is in the context of the
Ifk incident. The translation of "فإذ" as "so, when" or "Therefore, since" are both pretty good. Here are my observations given these two uses:
1. Contrary to a conditional construct (using "إذا" for example), this construct asserts that the statement after "فإذ" actually took place, and it took place in the time tense used.
2. Although it does assert that the statement after "فإذ" took place, this is not the main assertion of the construct, but only an explanation for the main assertion to follow.
3. The main assertion is what would follow after the second "ف", which is the command to uphold the prayers in 58:13 and the statement that those people are liars in 24:13.
Therefore, I believe it is air-tight that the wording of 58:13 does not remove the obligation of 58:12. It provides
after-the-fact relief and means of repentance for those who didn't follow 58:12. I can see how people could violate 58:12 by simply putting themselves under the hardship exception in it without full justification (although this would not be blatant violation since hardship is subjective), and that's perhaps why blanket forgiveness was given and the repentance mechanism ordered was nothing more than doing the duties they would do anyway.
BTW, I think the role of 58:12 was to reduce the load on the Prophet (PBUH) which was getting out of control. People probably approached the Prophet less after 58:12, either because they didn't want to give charity or because they weren't comfortable using the hardship clause. The end result was the intended one, to put the brakes on a work load that was going out of control.