There is a "DS File" Synology app to browse your Synology NAS via your Android phone, but the app is really laggy etc. On Samsung phones there is the "My File" app, a file browser that really does the job, and that would be perfect could it browse the NAS. (In fact I already tested it when the phone is on the same (wifi) network as the NAS as the app allows it with the "connect to a network drive (SMB)".)
Now, the app also allows to connect to an FTP or SFTP server. Hence in Synology I did a "control panel -> FTP -> Enable SFTP server" with port number 16666 (in the range allowed by my router) and a "control panel -> Terminal & SNMP -> Enable SSH Service" with the same port. Then I said to my router to forward that port.
In the "My File" app, I did an "add SFTP server" where I added the IP address from the Synology NAS, the 16666 port, my admin user name and password, and I keep having an error not allowing me to connect.