I did tameshigiri for the second time last night. Speaking as someone who regularly practiced zazen for 15 years it is an incredibly Zen meditative experience!
Just because you could match your meditation experience to your martial arts experience does not imply that there is something unique to martial arts going on. As I mentioned, almost any simple physical activity may become a meditative practice and may benefit from such practice. I like the following quote about zanshin (from https://wwzc.org/dharma-text/zanshin)
"In taking a step, it is the weight rolling smoothly and the next step arising. In breathing in completely, it is this breath. In breathing out completely, it is this breath. In life, it is this life. Zanshin means complete follow through, leaving no trace. It means each thing, completely, as it is."
"In taking a step, it is the weight rolling smoothly and the next step arising. In breathing in completely, it is this breath. In breathing out completely, it is this breath. In life, it is this life. Zanshin means complete follow through, leaving no trace. It means each thing, completely, as it is."