It is possible to have only one Azure application for both a bot and a tab app. However, it is not recommended as it can cause issues with authentication and identification of the current user. It is recommended to keep them separate as the Teams Toolkit does by default.
Regarding the error message you are receiving, "InvalidStaticTabUrl", this can occur if the static URL in your manifest file is not valid. Make sure that the URL is using HTTPS and is either the same domain as the settings page or specified in the manifest's validDomains
list.
As for your attempt to use the "app-name-aad" settings on "app-name", it is unclear what changes you made to the manifest file. However, it is recommended to keep the two applications separate as mentioned earlier.
References: