I often feel the exact same way. I have had to really be honest with myself to understand these feelings. What I have realized is that this feeling can mostly be reduced to fear. Fear of becoming obsolete, fear of being not so smart, fear of not being a "real programmer". It also doesn't help that a lot of people in other fields really do look down on web developers in this way. At least for me, this induces a fear response and I get anxious and it is almost entirely out of insecurity. I start to "stress learn" things that I feel would make me a "real programmer" even if I have no real use for or interest in them. It's pointless, of course, but I have found it to be a viscous cycle that's hard to fight sometimes.
A few things have helped me. The first is that you need to embrace what you do and love what you do. It doesn't sound like you hate being a web developer, more that you feel you should be doing "harder" things. Web development is far more than CRUD apps, so it might be worth looking for another job that will challenge you more as a web developer.
The second thing is that you need to understand what you do _deeply_ instead of _broadly_. I have for a long time considered myself a generalist, but this has its drawbacks. When you really understand a tool set deeply and become an expert a lot of the lower level internals really reveal themselves. You end up learning things that you've always thought you wanted to learn in isolation, but instead there is now a useful context in which to learn them. Not to mention that this helps with the feeling of being "not so smart" because you will form informed opinions as a result of your deep level of understanding.
The last thing is that you do need to feed your curiosity and the only way to do that is through projects. You want to build a compiler, build an emulator, a game engine, a database, or an OS? You really just need to do it. I have dabbled in each one of these things. Some of which I got very deep into, others not so deep. Each time I learned a little bit more. The hardest part is picking a project and running with it, especially when there are so many different options, but it is the only way.
Sometimes it's important to take a step back and appreciate what you do. It's very easy to beat yourself up and compare yourself to others. If you really are unhappy with what you do, then you need to start deeply diving into something that you do find interesting. Nothing in this field is easy and it all takes time to gain any level of proficiency at.
A few things have helped me. The first is that you need to embrace what you do and love what you do. It doesn't sound like you hate being a web developer, more that you feel you should be doing "harder" things. Web development is far more than CRUD apps, so it might be worth looking for another job that will challenge you more as a web developer.
The second thing is that you need to understand what you do _deeply_ instead of _broadly_. I have for a long time considered myself a generalist, but this has its drawbacks. When you really understand a tool set deeply and become an expert a lot of the lower level internals really reveal themselves. You end up learning things that you've always thought you wanted to learn in isolation, but instead there is now a useful context in which to learn them. Not to mention that this helps with the feeling of being "not so smart" because you will form informed opinions as a result of your deep level of understanding.
The last thing is that you do need to feed your curiosity and the only way to do that is through projects. You want to build a compiler, build an emulator, a game engine, a database, or an OS? You really just need to do it. I have dabbled in each one of these things. Some of which I got very deep into, others not so deep. Each time I learned a little bit more. The hardest part is picking a project and running with it, especially when there are so many different options, but it is the only way.
Sometimes it's important to take a step back and appreciate what you do. It's very easy to beat yourself up and compare yourself to others. If you really are unhappy with what you do, then you need to start deeply diving into something that you do find interesting. Nothing in this field is easy and it all takes time to gain any level of proficiency at.