Secure ShellFish is a SSH and SFTP file manager that works well with other apps.
Setup new servers inside Secure ShellFish itself and access files on these servers in the Files app and other apps supporting the document browser or document picker. Applications that can open files or directories in-place such as Textastic, iA Writer, Pythonista and many more can work directly on your server.
Files are downloaded on demand and uploaded when there are changes. In case of networking errors the uploads will be attempted later when you get back online.
Secure ShellFish is a premium app that is free to evaluate. You will be able to configure servers and try out the main features of the app before paying, but every once in a while you will need to extend your evalution. When you are certain you like the app you unlock permanently with a one time in-app purchase.
Once the app is unlocked you can configure files or directories to be available for offline access. The app will download these things beforehand and keep the local copy and remote copy in sync.
Both your iPhone and iPad will get SFTP capabilities. Unlock is shared with other devices logged into the same App Store account and server configurations are shared between devices if you have iCloud keychain enabled.
Access files on your Mac by enabling "Remote Access" inside Sharing preferences. If you local network supports Bonjour the Mac appears automatically making first connect easy.
The app works with Synology and other NAS solutions for fast file access at home or the office even when Internet is lacking.