For quick graphical management I use FX File Explorer because it keeps the timestamps when moving files.

For something more I use... Termux. I like to sort things based on timestamps as well, but often I like to set some custom modification time, or copy modification time of a file being replaced (e.g. replacing old 128kbps MP3 for FLAC), and I don't know of any other way than touch.
Similarly I don't know what else to use for syncing directories other than rsync.
Plus, I can run SSH in Termux, that means Rsync-ing between PC and my phone is pretty easy.
And it also means I can mount the phone over SSHFS (granted KDE Connect already takes care of this).
I can also use GPG for encryption and decryption of files.
And Vim works fine for me for text editing too.
And now since I already have that, say I want to access some files on any computer. It probably has a browser, and Termux has NGINX, coupled with FancyIndex it gets pretty nice for file access. I like the Material theme.

Now, a bit of a disclaimer: BE CAREFUL WHAT ADDRESSES THE PHONE IS LISTENING ON
I set them manually rather than the typical default of all interfaces. Unfortunately, Android seems to have no firewall. I can easily reach things on my phone connected to mobile data thanks to IPv6. This may or may not be desired. Oh, and NAT isn't for security either, so don't think you're safe because you only use IPv4. Perhaps devices behind same NAT aren't isolated.

Edit: Example of the WebUI with Material theme (sorted by date because I was able to set the file timestamps):