So long as you don't believe in even one deity, you're an atheist. Whatever else you're on about is your business.

As to whether it's logically consistent to be an atheist and pursue "spirituality" depends on your reasons for being an atheist and your definition of "spiritual". If you're an atheist for considered reasons you're generally a skeptic and a critical thinker, at least relatively. This means that it's logically inconsistent to believe in a spirit or soul or other supernatural entities because they're as unfalsifiable and unsubstantiated as any deity.

On the other hand if "spiritual" is just a way of saying that you're a deep existential thinker or pursuing mindfulness or some form of "mind expansion" such as "peak experiences" of non-duality or some such, then that is not necessarily incompatible with critical thinking. It does get into the realm of personal subjective experiences that it's easy to be deceived by and easy to take too seriously / overthink. So long as you are an objective observer and don't draw conclusions other than what is clearly warranted, it's still possible to be a critical thinker and to be logically consistent with what I'd call considered atheism.

People do in my experience strongly tend to try to resolve and explain the unknown and have not learned to sit with uncertainty. As such, they tend to find it irresistible that anything that falls into the category of "unexplained" finds a pattern match in whatever form of woo they are personally or at least culturally familiar with. I once was at a public "ghost hunt" (my stepson likes that sort of entertainment) and I noticed that there were Christians, Spiritualists, New Agers, Pagans, etc. and each of them tended to ascribe perceived supernatural events in terms of their preferred belief system. It was rather entertaining to hear them relate campfire stories that were invariably connected to their mythos of choice and interpreted / understood differently by members of each group. My stepson and I seemed to be the only ones who were making an effort to keep an open mind and to consider alternate hypotheses (ultimately I concluded the most likely explanation for the truly unexplained events of the evening was the Ideomotor Effect).

So my advice for the "spiritual" atheist is to learn to say the magic words "I don't know and I can't say" when the unknown is encountered, until you have some actual preponderance of actual evidence to work from. Understand in advance that some things will never be explained, at least in your lifetime, and that's okay.

Another angle on this can be had from the book The Little Book of Atheist Spirituality by Andrew Compte-Sponville. This is taking spirituality to mean "pursuit of the great virtues" and it lays out an ethos of kindness, honesty, integrity, etc., as a "spiritual practice" based in objective facts and observations.

I have had a small number (maybe 3 in 74 years) of experiences similar to those described by others here - that sudden sense of being at one with your surroundings or something that is happening. It is hard to know what to call it other than a spiritual experience, but it is apparently common to all sorts of people all over the world. Those who want to, identify it as a religious experience, but as a life-long atheist I assumed it was just a rather nice trick of the brain. I wish it happened more often but it isn't something you can bring on yourself, I don't think.

As I see it, the physical world of our senses is not real, though we have become so habituated to it that it seems like reality. Our perceptions are based on the model of matter moving in space and time, but that is just a mental model. We can experience true reality only indirectly, and even then have only a brief taste.

If you think of “heaven” or the Spiritual as being a higher realm outside our normal experience, then we are in heaven all the time, but have only tenuous awareness of that reality. In this version there is no such thing as the supernatural, but there is an aspect of nature that we can not understand with our normal space/time/matter mental model.

I am brand new here, but don’t really identify as an agnostic. I’m not anything, except bewildered and amazed by the mysteries of existence and consciousness.

I hope y’all do not object to the presence of a non-agnostic.

Yes. I’ve had the experience of “oneness,” first with another living creature, then with all that surrounds me. I was lost in thought one day on my back porch when I saw a mourning dove in my yard. My focus shifted to the bird, one of my favorites because of its call, and when I lost my sense of self, I felt as though I had connected with the bird and become one with it. It was such a peaceful feeling, but I lost it the minute I became conscious of myself again. Focusing again on the bird, I became acutely aware of how interconnected and interdependent we are with all that surrounds us. I felt the flow of energy extending through me and to all that was around me. It was exhilarating! That was the closest I’ve ever come to anything “spiritual” like.

I'm not sure one has to have a "spiritual experience" to consider themselves to be a "spiritual" person. I think there are many definitions of spirituality.

Some might consider it to be a feeling of connection to the source of creation, or their environment, to humanity, or to the past, present and future. Some might consider it to be open to being inspired by literature, poetry, art, mythology, or nature. I don't believe in "a spirit" or a physical "soul" as many religious folks do.

The word "spirit" actually comes from the latin for "breath" and is thought of as something you can't see but gives you life. Here in Hawaii, the term "aloha" means to share the "breath of life" from one person to another.

I see being "spiritual" as a feeling, or a connection to the greater humanity or cosmos. Just something through which you see beyond yourself. I believe you can consider yourself to be "spiritual" while not believing in supernatural deities.

The word "spiritual" can mean almost anything to anyone. I take care not to use the word as if I use it it will be understood differently by everyone who hears it. Spirituallity is usually believed to be some sort of magical power or spirit. It can also be used or understoood in a purely emotional since. I do not believe in any super natural, magical spirit. When I was a child I was indroctionated into a fundamentalist, extremist Methodist church and convienced by my elders that emotional experiences I was coached to have were GOD.