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fix(docs): keep search responsive and contain sidebar scrolling #1364

Job	Run time
docs changes	27s
docs benchmark (${{ matrix.target }})	0s
docs source	1m 45s
docs build	1m 50s
docs acceptance (corpus)	2m 15s
docs acceptance (http)	2m 1s
docs acceptance (chromium)	2m 22s
docs acceptance (webkit)	3m 14s
docs HTTP	3s
	13m 57s