How to avoid dumping data from big tables (like `report_viewed_product_index`) using MariaDB?

Use the --ignore-table-data option.
E.g.:

(
	export TZ='UTC-3';
	db=$(my_print_defaults mysql | sed -n 's/^--database=//p')
	mariadb-dump \
		$db \
		--ignore-table-data=$db.report_viewed_product_index \
		--ignore-table=$db.search_query_backup_20250909 \
	| sed -E 's/DEFINER=`[^`]+`@`[^`]+`//g' \
	| gzip > ~/$(date '+%Y-%m-%d--%H-%M')--production.sql.gz
)