Does the と変わらない mean "the same as" here? If not, how should I interpret it more accurately?
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Basically yes, the structure of the sentence is [砲撃にあたり...必要なの] は 長距離砲兵型と変わらない. So literally, That (it) requires ... is not different from (the same as) 長距離砲兵型.
Another slightly different parsing would be to interpret 必要なのは as a topic describing the aspect of difference: in requiring .. at the time of firing, (it) is the same as 長距離砲兵型.
In terms of translation, translating と変わらない adverbially may fit more easily, so it is just as rather than same as: (It) requires .... in firing, just as 長距離砲兵型.
Your interpretation is correct. To be precise it's "not different", but "not different" is not different from "the same as", so your interpretation is not wrong, which is not different from correct. There are reasons we use expressions like double negatives, so the author probably has its reasons to chose 変わらない over 同じ.
This could be written verbosely. I assume something like:
(The fact that it needs 前進観測機 for 砲撃 is no different from that of the 長距離砲兵型's)