For me, the most important part in magic is interaction with the audience. But how to practice routines that are created for audience Involvement in front of my mirror?

Provided you have the mechanics down for the routine and are very comfortable with the moves and sequences, I practice as if there were people actually in front of me. I also verbalize what is to be said, (Patter/script) BUT there is no substitute to getting in front of an audience. Sooo many different personalities and depending on the venue, you have to be worth watching, deal with distractions/attention spans and know how to aproach people in the first place.

Restaurant work- table hopping / strolling / walk around / formal/ parlor / stage etc. all have their own challenges. I've read all the books, watched all the videos, which did help me intellectually, but again, it was getting out their, performing that really made the difference.

You can only go so far in front of a mirror. Interacting with real people, there is no alternative.

There are also many "audience involvement" skills that can be practiced without magic tricks. Developing vocal control of pitch, volume and timing
can be practiced by telling stores or reading poetry out loud and observing spectator reactions, for example.

Later on you can vary your magic effect presentation based on non-verbal cues from the audience.

Also, many hand, arm and body postures/positions can be practiced all day long in many activities until they become the "natural you."

A magic book might say, "Let you arm fall naturally to your side." What is natural for you? Practice can make it so.

The point is that "audience involvement is just part of "audience engagement."

Expanding on David's great advice,

If one is not comfortable with interacting with people live in normal settings, trying to do so during a magic effect will be difficult.

Perform for an imaginary person & imagine how he would respond. That's how I practice

Great advice in this video by Mr. Williamson https://www.youtube.com/watch?v=Ar_c5kdHKew&t=396s

Yes Yes Yes