Optimizing number of printing pages in QGIS

You can use the Atlas function in QGIS and select the layer with your features (the blue lines in your example) as coverage layer. Than QGIS prints a separate page for each feature and fits all the features to the page (with the option to define an additional margin).

If you want to create something like a grid, but only get a cell for each feature and one that is oriented in the right direction, use Menu Processing / Toolbox / Minimum bounding geometry, see the output: yellow polygon layer, let's call it cover. This layer will be used in the atlas instead of the grid, where you would need not less than 9 pages.

You can now use this layer cover as cover layer for your atlas, so no empty pages will be created and the features will all fit exactly on the page. To rotate the page, set map roatation to data driven override in the element properties and paste an expression like: 90 - main_angle ($geometry):

And this is the oupupt of the atlas: two pages with features fitting (+1% margin). The north arrow shows you the rotation:

page 1:

page 2:

page 3: