There are multiple different types of Firefox extensions. The most likely reason you are not seeing a manifest.json is that the specific add-ons which you are looking at are not WebExtensions. Basically, if it was a WebExtension, it would have a manifest.json. The fact that it does not have a manifest.json, means it is not a WebExtension. WebExtensions have only existed for a relatively short period of time. The significant majority of extensions will be of other types. The Introduction to Firefox add-ons provides some brief information on the files used in the different types which may help you identify the type of add-on you are looking at.
Without you providing the code for the add-on in the question, a pointer to the extension on AMO, or, at a minimum, a list of the files contained in the extension's root directory (which may, or may not be enough), there is no way for us to say what type of add-on you are looking at.
Using web-ext
is not possible on other types of add-ons. If the add-on is restartless (i.e. does not require you to restart Firefox in order to install or uninstall it), you should be able to load it as a temporary add-on from about:debugging
.