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Workers may prefer a tray that matches with paper sizes, which vary based on the business and to a lesser degree the operational requirements of a company.
Does the bold part mean "the paper sizes vary based on the business, and it also varies based on the operational requirements of a company, but it's degree of variance is lesser than the one based on the business"?
Does the bold part mean "the paper sizes vary based on the business, and it also varies based on the operational requirements of a company, but it's degree of variance is lesser than the one based on the business"?
Yes, that's exactly what it means.
I would have punctuated the original sentence as:
Workers may prefer a tray that matches with paper sizes, which vary based on the business and, to a lesser degree, the operational requirements of a company.
where the commas make the phrase "to a lesser degree" operate as a sort of parenthetical, and thus make the sentence easier to parse.
You can see clearly that there are two reasons why the workers' preferences might vary: business concerns and operational requirements. Then, from the parenthetical "to a lesser degree", you can tell that the second concern (operational requirements) is less important than the first concern (business).
The phrase "to a lesser degree" is a common idiom in the English language. The adjective "lesser" could also be substituted for "greater" to invert the meaning. You also commonly see "extent" in place of "degree"; this has essentially the same meaning.
You can read "to a lesser degree/extent" as "less than"; "to a greater degree/extent" can be read as "greater than" or "more".
