I believe that each one of the surahs in the Quran focuses more on a specific topic, otherwise it might be repetitive to read the same thing over in every surah. But sometimes it feels like many surahs are mentioning very similar things or bringing up similar stories. If not thinking about a surah as a whole, then it might be difficult to understand what the surah emphasizes.

Am I misinterpreting?

Some surahs are easy to follow and understand the story, for instance surah Yusuf. It is easy to follow because it is written in a chronological order. But for some other ayahs, it is not as obvious as in surah Yusuf. Hence, I had such interpretations in first paragraph.

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In fact, the holy Quran emphasizes and sometimes repeats the same topics, subjects and stories due to importance of the message that lies in those things or sometimes Quran tells a story but means the same characters found in all eras like Moses and pharaoh. There are some books written or compiled especially in Persian that which topic or topics the each surah emphasizes on or discusses. Yes, you are absolutely right that we should look at every Surah as a whole to understand what the surah emphasizes most. In some Surah there is a story so it's verses are put in chronological order like Surah Yusuf but overall the place of verses in Quran is "tauqeefi" (meaning the verses were put in the suras as per order of the Holy Prophet (PBUH) to his companions according to the guidance of Gabriel) therefore the sequence of the verses is not the same as revealed on Holy Prophet (PBUH) so it may felt sometimes when reciting and reading the meaning of a Surah that the sequence is broken.