When the recipe allocates 8 minutes for browning the beef, does that mean 8 minutes per side or 8 minutes total (so about 2 minutes per side)?

The important part is that you brown the beef, however long it takes. The time that the person giving the recipe is based on their technique, stove, pan, oil, beef etc. etc. As you probably do not share those items, time becomes a massive variable that should be discounted in favour of the desired result.

My interpretation is the browning/searing process for a 3 lb tenderloin should take you about 8 minutes total.