how to send group email, while hiding recipients address

put the recipients' addresses in the Bcc: field.

BCC for the recipients, as mentioned above.

For the sender...

All mail messages have a sending address and a reply-to address.

You can set up from-address aliases in mail, but some source info will be in the message.

https://www.macobserver.com/tmo/article/Using_Multiple_Reply_Addresses_In_Mail

Or send your message from a privacy-protecting mail service.

Which’ll still have origin info, but less likely to be tied to you.

iCloud also allows mail aliases: Use email aliases on iCloud.com - Apple Support

A mail server service is another potential option, as a mail server can be configured to only send messages from the list, and not from the submitter.

Note that most ISPs have limits on the number of recipients to curb the outpouring of spam. You will need to check with them both for number of max. recipients and max. number of emails per day.