The illustration above is the setting I remember from confession. The contemporary format of sitting on either side of a table out of Starbucks shop with no obscuration keeps me away from the sacrament.
You picked up on the “alter Christus” in the picture, then?
The priest acting in the place of Christ.
In most reconciliation rooms there are two chairs, one openly sitting next to the priest, then one behind a screen. The latter is situated so that you walk in and are not seen by the priest at all. You can come and go incognito if you prefer. Do not let that keep you from the confessional. Check out the room at your church or the church you will go to ahead of time to be confident and assured that you can go anonymously.