This is correct. An addition: the working profile should be large (e.g. Rec2020 or ProPhoto), the output profile for web should be sRGB, and for print you ideally need a specific printer profile for your printer, or any large profile with the caveat that you need soft-proofing if you want to emulate how your print will look like. In both cases you can deviate if you’re sure about what you’re doing.
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