Amaze supports the features you've listed (tabs and SMB shares), as well as root access, and has a clean user interface:
After a bit of digging, it looks like Amaze is limited to 2 tabs, which you switch between by swiping left and right. I guess that's technically "multiple tabs" as their Play Store listing states.
There's also Ghost Commander if you're looking for an open source file manager with more capabilities. It uses a 2-panel layout, supports plugins, and has a long list of features:
https://f-droid.org/packages/com.ghostsq.commander
https://play.google.com/store/apps/details?id=com.ghostsq.co...
If you need a file manager that supports 3+ tabs at once, I don't think there's an open source solution right now.
Do you rather have an app on your phone with access to your files that most probably runs dubious software alongside? Or, do you rather not miss out on the elegance and convenience it provides? I guess the answer depends largely on the content of your files and your personal preferences.
Also, Google hasn't flagged the app, which I believe they would if it was malicious as opposed to made by a company that had issues in other apps. So unless there's specific malicious behavior tracked, which I don't see, I'm not going to get rid of it.
"The Lumen Privacy Monitor" developed by the ICSI Haystack Project collects statistics of outgoing tracking traffic and their app origin on your device.
They have good intentions, e.g. with a system level image picker, but it's UX is one of the worst among the system level components.
Do you want your folders to be organized/displayed different?
Or you want this integrated without having to download an app?
To come back to the photos example, by default Android has a Document picker. Its .. bad. Unless you are picking a picture you have just taken, you won't be able to find what you are looking for.
At the very least, either allowing apps to respond to the search intent in order to allow them to handle the search however they want or at least delegating this task to one app (like Google Photo) that already has a good search feature.
More generally, I am not a big fan of exposing the file system to end users. It is relatively convenient for power users, but for all the other users it is a complete mystery.
For pretty long, Android has toyed with the idea of doing something else. Hiding away the file system as an implementation detail users don't need to know and offering a document based interface instead.
Whether this could work or not has remained unanswered though .. their implementation is so half assed that it is barely worth mentioning.