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They are all grammatically correct (aside from the spelling of disappear). I would say the best of the three alternatives is
- Some manual jobs would disappear in the era of AI.
However, the use of "would" suggests a counterfactual: that you may believe it may not happen, won't happen soon, or is very hypothetical. That might be consistent with using "an" era of AI, as if there may be a few eras of AI in the world's history, but they aren't very transformative or impressive. I don't think that's what you are trying to communicate.
I think a better way to say this is
Some manual jobs will disappear in the era of AI
or
Some manual jobs will disappear as we enter the era of AI
The latter implying that once we enter the era of AI, it will be a part of our lives (and economy) forever.
Good question - it addresses the importance of detail in statements such as these, especially when small adjustments can develop noticeable implications. Farnsy covered an important point about use of "would" versus "will" as well, and if your intention is to imbibe your sentence with a feeling of inevitability, then it is worth considering.
Regarding "an" vs. "the" vs. "a new", however, I would add that each comes with its own, albeit small, implication, that does have a chance to tune your message further.
(1) Use of "an era" implies the viability of many possible AI futures, making them act as an indefinite reference for the reader as the specific details of this future are unclear/unspoken.
(2) Use of "the era" implies that there is only one AI future (which is known to the reader as well, making this a definite reference), and/or perhaps it encompasses all possible options, and that loss of jobs will occur within it being realized.
(3) Use of "a new era" implies that, in this case, we are already in an era of AI, and the "new" AI era would be coming up next.
Overall, I believe that either (1) or (2) would be perfectly reasonable for your purposes, and could be used based on your choice of the implication you may prefer. Sentence (3) could be used, as it is a proper sentence, but it makes a secondary implication about our current day and age being one of AI already, which would require further supporting information prior to making that statement in order to convince the audience.
Hope this helps, and let me know if any further clarification would be useful!
P.S. Here is a reference if you would like further reading on the definite/indefinite reference idea (essentially tips on usage/non-usage of "the") - http://www.law.cuny.edu/legal-writing/students/multilingual/grammar/articles.html
