I put some time into this last night before I fell asleep.
You insist that "belief is a form of worship." It might be argued that is the case in a religious context but absent that context, belief and worship are without question two distinct concepts.
I believe it is just the opposite! What is worship without belief in the supposed doctrine?
It's fairly common, really. I attended church for several years and participated in many, many acts of worship, even though I didn't believe. I know I'm far from the only one who did so. Pro forma ritual is a big part of religion.
No.
Mediocre "religious" people are inclined to describe the activities as two distinct categories, because their church/organization is inclined to present a package of activites that they are going to describe as "worship services." The more keen theists recognize that belief is the essential part of the activities that "converts" the activities to worship.
You bought in to the church's description of "worship services," as being a distinctly different activity from belief, because it fit your needs for this debate. Chances are you have never had to debate an atheist over the definition of religion - I have never encountered an atheist who is willing to buck the dogma, like me. No atheist has ever joined in to support me, never before, and it will not happen here, either. Even if you are inclined to change your mind about the issue, you are not going to reveal that to the other members, because it elevates my credibility on other issues, and relatively lowers your leadership qualities; which is what is encountered at the atheist organizations - people at the top want to stay at the top, and are not inclined to reveal to the peasant members that there are problems in the established doctrine that has kept everybody happy for the longest time.
Atheists reinforce the dogma when they use the erroneous definition when debating theists who claim that atheists have a religion.
Atheists do not believe or worship gods - can't have a religion
The problem is you probably attended the services to appease your relationship with someone who expected you to participate, and that is worshiping the doctrine of the relationship; but your participation in the activities was not a form of worship of the gods; although, it was in tacit support of the church's membership campaign.
You neglected to consider the reverse of your question. Even in a religious context, there is a multitude of people who sincerely believe in a god, yet never perform a single act of worship. Even if they were to get dragged into a church service they'd only be in the presence of others who were worshipping, and likely resenting every minute of it. They'd be hard put to participate; wouldn't know the words to say, and would probably only be able to sing along on some of the songs. You may not acknowledge that belief can exist without worship, but you don't dictate what goes on in other people's heads.
Attending the services under contest is not worship. If a person describes them self as believing in a god, then that is worship (proselytism) - they are disseminating the information that there is a god. The purpose of overt worship (activities) is to promote the doctrine. The people singing in church are unwittingly promoting the church's activities to gather membership of people who want to sing and do the other activities that the church packages - they call it worship, because they attach a deity to their doctrine for organizing community.
It is amazing that you do not recognize the misplaced definition(s) that have formed the dogma that keeps atheists in the theists' "box," because you are very smart.