As for your approach you are right I think. Creating content in Microsoft Teams Wiki means it gets stored in underlaying SharePoint Online site in library "Teams Wiki Data" as .mht files. You can open them in SharePoint Online by click, but they will sadly open in your client software "Microsoft Word".
How we solve sharing information between "Microsoft Teams" and connected "SharePoint Online Site"
As you know - creating a team in Teams means there will be created a SharePoint Online site with same permissions. This is the technical base of storing data in this team.
With the site a "Notebook" is created. This is a OneNote notebook and this can be used in both worlds - in SPO and Teams.
To use this for storing information as you would do in "Wiki" just add a tab to your team channel by clicking the + symbol.
Then choose OneNote as app to add.
Choose "browse notebooks" to get a selection of OneNote notebooks on your connected SharePoint Online site. Select the notebook you want to use in Teams and SPO for storing information.
OneNote provides the same functionality as the Wiki tab in Teams and gives you the desired option to be used in both worlds without problems.
Maybe this helps you out. Would be pleased if you marked this as answer if this helps.