Is there any way of having a scrollbar or search bar for an attribute section?

Yes, if you have a lot of attributes, our Improved navigation extension allows choosing an appropriate view of attribute values: a search bar (1), a scroll bar (2) and/or a show more/less option (3). Here is an example:

Magento Improved Layered Navigation - Amasty

See more details on Improved Layered Navigation page
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