Interesting question indeed, and I have never used Jira for those purposes. Correct me if I am wrong, but you are asking which product would suit you the best, so let me summarise:
Jira Software - mostly focused on project management which is used by a lot of software development teams (not limited to)
Jira Service Management - mostly used by IT support and customer support teams (not limited to)
Jira Work Management - this would interest you the most, it comes free with Jira software and is more focused on the business teams
Trello - visual project management tool - simplified version of Jira Software