When you talk about financial cloud management the ABC of it is always tagging. So that is definitely important.

Your approach makes total sense. I would not recommend any third party applications as they always require you to spend about 1,5-3% of your total yearly cloud cost. So when you grown, you immediately need to pay them more as well.

What I would do instead, is use AWS Quicksight, they have about 9 different pre-configured dashboard that help you get all the answers you want. The best one that fits your use case of multi-cloud overview is the CUDOS dashboard.