Continue Numbering is actually part of the Paragraph Style.
When you apply Continue Numbering, notice that a
+ is added after the name of the Paragraph Style. It is seen as an Override.
So you could just hit the Create new style button in the bottom of the Paragraph Styles panel to create a new style based on the numbering style, which will continue numbering.
So you have a "mother style" which is only applied when you want numbering to reset and another style which you use all other places.
This setting is located at Paragraph Style Options > Bullets and Numbering > Numbering Style > Mode. The options are Start At (followed by a certain number) or Continue from Previous Number.
With multiple levels it can become a little convoluted and multiple styles might be needed. The Restart Numbers at This Level After setting can come into play.