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- Today I've done something that I've never done before.
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- Today I've done something I never did before.
Both 1 and 2 are natural, and a fluent speaker might say or write either , and would surely understand either. also possible would be:
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- Today I've done something that I never did before.
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- Today I've done something I've never done before.
In sentences 2 and 4, the omitted "that" is implied.
There is no rule of grammar that the verb tense in the first part of the sentence match that in the second part. In fact there can be more glaring mismatches, such as:
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- Next week, I expect to do something I've never done before.
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- Last month I did something I've never done before.
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- Later that year, he would do something that he had never done before.
This is one of many cases where people invent or repeat "rules" that are not rules at all. The supposed rules hold true in many common cases, do people assume they cover all of English, when, in fact, they do not.