I have to admit I haven't been buying a lot of new apps the last few years. I don't play games on my phone and most of the apps I use daily are basically the same ones for a few years already.
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FX file explorer An excellent file manager that I have been using since forever. There are other good ones, such as Solid Explorer, but FX is my favorite.
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Tasker I used to play around with this so much, the things you can do with this app are endless. But I have been using it less lately, switched to Google home since it has better/easier integration with other devices in the house.
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Nova Launcher I think most of you will be familiar with this launcher. I have probably been using this one since it came out. It's perfect!
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JuiceSSH Pro To be honest I don't even know what features are unlocked by purchasing the pro edition without looking because it has been so long since I bought it. It's an SSH cliënt and one of my most-used apps.
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Sync for Lemmy There are plenty of Lemmy apps that are good but I was using Sync for Reddit since forever so I jumped on the hype-train when it came out. I paid for Ultra monthly because 2€ per month for something I use daily is a no-brainer.
Besides these there are some Google Wear watch faces I purchased. There had been other apps that I bought years ago like sdmaid or some other tools from when I used to install custom roms but I don't really use those anymore - too much hassle for marginal improvements. And the question was about apps that are still relevant.