How to alter my expression to return the same result while being compliant with POSIX BRE / ERE?

I'm trying to use Snowflakes regex implementation, which I have just discovered is POSIX BRE/ERE. I had previously fashioned a regex expression to allow me to identify all commas not in double quoted string sections with a custom delimiter (for text file parsing).

Sample text string:

"Foreign Corporate Name Registration","99999","Valuation Research",,"Active Name",02/09/2020,"02/09/2020","NEVADA","UNITED STATES",,,"123 SOME STREET",,"MILWAUKEE","WI","53202","UNITED STATES","123 SOME STREET",,"MILWAUKEE","WI","53202","UNITED STATES",,,,,,,,,,,,

Regex command and substitution (working in regex101.com):

([("].*?["])*?(,)

\1#^#

Regex101.com (and desired) result:

"Foreign Corporate Name Registration"#^#"99999"#^#"Valuation Research"#^##^#"Active Name"#^#02/09/2020#^#"02/09/2020"#^#"NEVADA"#^#"UNITED STATES"#^##^##^#"123 SOME STREET"#^##^#"MILWAUKEE"#^#"WI"#^#"53202"#^#"UNITED STATES"#^#"123 SOME STREET"#^##^#"MILWAUKEE"#^#"WI"#^#"53202"#^#"UNITED STATES"#^##^##^##^##^##^##^##^##^##^##^##^#

So, given that I am now belatedly discovering that I cannot use lazy quantifiers, can any uber-regex'ers advise on how I might alter my expression to return the same result while being compliant with POSIX BRE/ERE?

Solution

You need to

Convert the lazy quantifiers into greedy here as they will still match in the same way as with lazy quantifiers
[("] matches ( or ", you need to only match " with this character class, use " only.

The final POSIX ERE expression will look like

("[^"]*")*(,)

It matches

("[^"]*")* - zero or more occurrences of ", one or more chars other than " and then a " (Group 1)
(,) - a comma (Group 2)

NOTE: POSIX BRE expression will look like \("[^"]*"\)*\(,\) where capturing groups are defined with a pair of escaped parentheses.