I think there might be some confusion between individual bacterial cells and "Bacteria" in general. The link you shared is either oversimplifying to the point of losing touch with the truth, or they simply used inappropriate word choice. It's unfortunate that they didn't seem to include a primary source to backup that claim.
For a more general statement like, "Most bacteria have plasmids," I would interpret that as meaning plasmids have been found in most bacterial lineages, not necessarily that most individual bacterial cells have plasmids. But I could see how that might confuse some readers and/or educational content creators.
I will share this for reference. The distribution of plasmids is typically heterogeneous within populations, and variable between populations. For any given plasmid, it's common for only a fraction of the population to carry it. Sometimes nearly 100% of a population carries has the same plasmid, but in other cases it can be 10% or less. I would wager that it depends on how mobile that plasmid is and on the selective pressures specific to the environment in which they are living.
I have personally observed this heterogeneity even in laboratory strains under antibiotic selection. I once determined that less than 20% of my E. coli cells in a culture were actually carrying the plasmid under selection (I did this quick experiment because I was not able to recover detectable amounts of the protein that I was trying to express in my strain).
The reference I linked might be a useful resource for the OP. In case that link doesn't work, here's the reference.
Holger Heuer, Zaid Abdo, Kornelia Smalla, Patchy distribution of flexible genetic elements in bacterial populations mediates robustness to environmental uncertainty, FEMS Microbiology Ecology, Volume 65, Issue 3, September 2008, Pages 361–371, https://doi.org/10.1111/j.1574-6941.2008.00539.x