How do I revivify an old iPad Air Wi-Fi, if it is worth it?

I think your battery assessment is dead on. Although I will say for these iPads, they can take a long time to power on if the battery is flat. I would be sure you’re using at least a 10 watt charger (Apple ones will be labeled right on the wall bit otherwise wattage is just amperage x voltage). Leave it on the charger for a solid hour.

As for whether it’s worth it to revitalize, that’s a matter of opinion. It depends on what it would be used for. it is a bit of an older device, so it will not be able to get the most current iOS versions, and may not be compatible with apps. But it would likely still be serviceable for basic web tasks, social media, email etc… But due to potential app compatibility issues you may need to use the internet browser versions (go to facebook.com rather than use the app for example).

IFixit has Guides to help, and a whole kit with all the parts and tools you need to get the job done. iPads can be a bit tricky to repair since there’s a lot of adhesive to get the screen out, but if it’s not turning on now, unless there’s data in it you want, you don’t have much to loose.