Bdtyktl

I quote to this support document at Mozilla.org

Turn autofill on or off

1. Click the menu button Menu and choose Preferences.


2. Click the Privacy & Security panel.


3. In the Forms & Passwords section, put a check mark next to Autofill addresses to turn it on, or remove the check mark to turn it off.

I have a Privacy & Security panel but no Forms & Passwords section nor an Autofill option.

This is an updated version of Firefox on an updated version of MacOS.

Where are these options? Searching for them using the preferences search returns nothing.

No option to save address, credit card and other details

Where are these options? Searching for them using the preferences search returns nothing.

This is a new feature and may not be rolled out in your version of FireFox:

Nightly

Address Autofill: Available for all users.

Credit Card Autofill: Available for all users.

Beta

Address Autofill: Available for users using en-US build and located in the US.

Credit Card Autofill: Not available.

Release

Address Autofill: Rolled out to users using en-US build and located in the US.

Credit Card Autofill: Not available.

Source Firefox/Features/Form Autofill - MozillaWiki

Wasn't this available in older versions of Firefox, a decade or more ago!?

Not as far as I know. However, there were add-ons that autofilled forms.

The accepted answer explains why you may not be seeing the described feature, but let me clarify the feature, itself.

Web sites offer varying support for auto-filling entries. They can use an @autocomplete attribute on input elements, and those inputs are identified by
field name. Otherwise, the input fields are just "dumb" places on a page to type stuff. In some cases, the web site does not want specific information auto-filled; password verification repeat entries is often an example.

Form filler applications can remember what content goes in what input locations based on things like input sequence and page location. Firefox has never had that level of form fill capability. It has always been limited to identified fields that support auto-completion.

What is changing is the mechanism. Since 2009, Firefox recommended auto fill entries based on frequency and recency. If it came across a named, auto-completable field, it would suggest for your selection, values you frequently use for an input field of that name. You would select from suggestions for each input field as you came to it.

What is in the process of being rolled out is the ability to use form profiles for all of the address, phone, and email input items. People often have alternate information they prefer to provide in different situations, and you can create multiple profiles that contain these common standard input items:

You can then select a form profile for a web site and input everything at once. It does require that you create the profiles. As you identified in the question, you select whether the feature is active and create profiles in Preferences | Privacy & Security. As David Postill's answer describes, this is in the process of being rolled out and is not yet available everywhere or in every version.

Mozilla is treating credit card information separately. This new feature looks like it may be available only in the Nightly version at this time (see Mozilla Support and Mizilla Wiki).

Further reading at: ghacks.net