If you need Custom Post Types then you'll need to use Squarespace 7.0. This version is still available. The newer version of Squarespace (7.1) does not (and will not) have Developer Mode.
Are there plans to eventually remove 7.0 and developer mode completely at some point?
Why does version 7.1 not support develop mode?
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Are there plans to eventually remove 7.0 and developer mode completely at some point?