How can bash recognize regex groups? [duplicate]

Question

I am trying to use regex to match a filename out of a path.

#!/bin/bash
regex=[^/]+?(?=.zip)
path="/home/quid/Downloads/file.zip"

if [[ $path =~ $regex ]]
then
     echo "Found a match"
     echo $BASH_REMATCH
fi

I should get

Found a match
file

Instead bash gives me this error

another.sh: line 2: syntax error near unexpected token `('
another.sh: line 2: `reg=[^/]+?(?=.zip)'

If I put the regex in a quotes, it no longer is recognized as regex. I have zsh 5.8 and bash 5.0.16 and it doesn't work on both shells.

How can I get bash to recognize the regex or not give me an error for using regex groups?

Answer 1

#!/bin/bash
regex='([^/.]+)([.]zip)?$'
path="/home/quid/Downloads/file.zip"

if [[ $path =~ $regex ]]
then
     echo "Found a match"
     echo "${BASH_REMATCH[1]}"
fi

Using Charles' regex and ${BASH_REMATCH[1]} gives me just the file name without the extension.