Like this?

You can just grep the help output

$ rsync --help 2>&1 | grep -E '^ *(--append-verify|--progress|--archive)'
--archive, -a            archive mode is -rlptgoD (no -A,-X,-U,-N,-H)
--append-verify          --append w/old data in file checksum
--progress               show progress during transfer

So it should be possible to create a simple script to do that. Similarly one can output the man document as text to stdout, which in turn can be grepped. I have no grep command at hand to do this in a useful way:

man grep | col -b

Here's what I get in fish when I start writing a rsync command and hit tab to ask for completions:

❱ rsync --append-verify --progress -avz -
-0  --from0                               (All *from/filter files are delimited by 0s)  --delete                   (Delete files that don’t exist on sender)
-4  --ipv4                                                               (Prefer IPv4)  --delete-after         (Receiver deletes after transfer, not before)
-6  --ipv6                                                               (Prefer IPv6)  --delete-before         (Receiver deletes before transfer (default))
-8  --8-bit-output                          (Leave high-bit chars unescaped in output)  --delete-delay                 (Find deletions during, delete after)
[more lines omitted]

There is a Plugin for Zsh (ohmyzsh) that gives you that right in the shell. I use it all the time and rely on it. Don't have the name on my mind though, sorry.

Fish does this but is intentionally POSIX noncompliant so you'd wanr to keep the old shell installed if you run other people's script.