As long as you are flying for your 121 carrier, the recurrent training covers all currency issues. If you fly part 91 on the side, that is a whole different issue.

Delta's addendum on AirlineApps asks for the number of approaches in the last 6 and 12 months, so I log them all and report them on the addendum every time I update, which is about twice per month.

Yes, log approaches. Odds are you won't do that many of them since the new FAA standard for logging actual approaches is all the way down to mins.

Somebody just had to ask the question a couple years ago, so FAA HQ issued a legal interpretation...

You can use them for 91 currency too (not needed for 121, including 91 operations conducted for the airline).

Leg by leg, approach by approach.

Don't be lazy, it pays off.