As well as enabling map tips in the menu, you also need to select the layer in the layer list, as only tips in the currently selected layer will show. Having the layer visible is not enough, it has to be selected as well. Only one layer can be selected at a time for tip display (as of 2023).
There are also some known bugs in some versions that prevent the tips from being displayed, and some combinations between QGIS versions, Qt versions, etc. also prevent tips from appearing.
In my case, the version supplied by my OS was unable to show tips, however other people running the same version on different Linux distributions had tips appear fine (but their Qt and Python versions were different). When I ran a version inside Docker, the tips appeared just fine. So if you have no luck getting tips to appear, try some different versions (both of the app as well as Qt, Python, etc.)