There's at least one Finder extension that can add such a button.

https://github.com/Ji4n1ng/OpenInTerminal

I have [right-click/control-click] > Services > New Terminal at Folder

Is that standard now, or did I add it long ago and forget?

That is standard now. It wasn't when a started using Path Finder. I still find it slower than just having the button in the toolbar.

I keep terminal.app in the tool bar and just drag and drop the folder on to the dock where the terminal app is

I have something that serves a similar purpose - a shell script that calls out to AppleScript to get the path of the most recently used Finder window and returns it as a string:

    #!/usr/bin/env bash
    
    ####################
    # Description: Get the path of the most recently used Finder window
    # Author: Ancapistani
    # Version: 1.0.0
    ####################
    
    osascript -e 'tell application "Finder"'\
              -e "if (${1-1} <= (count Finder windows)) then"\
              -e "get POSIX path of (target of window ${1-1} as alias)"\
              -e 'else' \
              -e 'get POSIX path of (desktop as alias)'\
              -e 'end if' \
              -e 'end tell';

I have this saved as `fpwd` in my shell.

the problem with such approach is it leaves terminal item in dock. I use warp terminal and it is really annoying.

You can drag the folder into the Terminal!