How to show progress with GPG for large files

Piping data into ssh (like you did) is the right way of passing input data to a command executed via SSH.

The issue here is that gpg needs two input streams to read from:

• one (STDIN) to read the data to be encrypted,
• another one (the interactive terminal /dev/tty) to read the passphrase (which is why you need to pass the -t option to ssh).

If you conflate the two and try to use STDIN for both purposes, then a way to signal EOF is needed to separate the two inputs. However, ssh would read the end-of-file too, and close the forwarded input stream.

The only practical workaround I can imagine is save the data to a file and then encrypt it using gpg (requires two separate ssh invocations)::

pv file | ssh ... '(umask 077; cat > file.unencrypted)'
ssh -t ... 'gpg -se -r ... < file.unecrypted > file.gpg; rm -f file.unencrypted'

You should try

openssl enc -aes-256-cbc -d -salt -in "$input_filename" | pv -W >> "$output_filename"

From the Manual:

-W, --wait:

Wait until the first byte has been transferred before showing any progress information or calculating any ETAs. Useful if the program you are piping to or from requires extra information before it starts, eg piping data into gpg(1) or mcrypt(1) which require a passphrase before data can be processed.

which is exactly your case. If you need to see the progress bar, for the reason clearly explained by Weijun Zhou in a comment below, you can reverse the order of the commands in the pipe:

pv -W "$input_filename" | openssl enc -aes-256-cbc -d -salt -out "$output_filename"