Hi Aichbus,
I have a number of tripods, got my first one close to 20 years ago, that was one of those cheap, light weight aluminium ones, where to obtain eye level height, the centre column had to be lifted up. Such cheap tripods may have their place (e.g. for quick and dirty long exposures, etc). But for any truly serious photography, they are not worth it. So when you say/write: "I put the system on a small tripod, which easily vibrated when touched, but stood completely still when left alone." - that indicates that yes, your tripod is not up to the task (as Bennymiata, above, also points out).
My current tripods include 3 x higher end Manfrotto tripods, including the 055 Pro and the 190X Pros - which are really versatile and a great balance.
I undertake various different genres of photography, including landscape, night time photography and other long exposure. For best results, I use live view in my DSLRs (much better than the old "mirror flipped up" option) or my mirrorless cameras, I also use a 10 second self timer because in some situations, 2 or 3 seconds isn't long enough. In other cases - though - and for the most overall convenience) - I advise the use of a remote shutter. That avoids any jittery vibration from touching the camera / pressing any button.
(Hopefully you also know that using back button focus - rather than using the half-press of shutter button - to obtain autofocus, is by far the best option here too... I went BBF about 15 years ago, and have not looked back since... pun intended!) Though for many of these types of images, I often use manual focus and/or do focus tweaking. The 5x and 10x preview in live view and/or mirrorless is a real treat to do this in the Canon bodies!
Higher pixel density is more telling of any shake / vibration, etc. The recent cameras are more critical of any camera shake compared to earlier / lower megapixel cameras. The M6mkII is in the higher pixel density (recent camera) category. And yes, I understand why with a 0.8sec exposure, it would show some vibration - even after 10 seconds, from the mechanical shutter if you are not using a very solid setup overall. If you are taking photos indoors, even people walking in another room or a different floor, and opening/closing doors etc can lead to noticeable vibration. Bridges, proximity to the road and other aspects can introduce unwanted vibration too.
I can obtain perfectly sharp images with pin-point features (obviously given focus is nailed and the subject is perfectly stationery) for exposures of up to a number of minutes. My Manfrotto cameras are very good. As bennymiata wrote above, carbon-fiber can help with vibration dampening even more than a good aluminium one. Though the most important is to ensure you have a sufficiently sturdy and "pro" tripod, and how it is placed is solid too. I have not needed a carbon-fiber tripod to date to obtain images that I am very happy with (and I am very critical of image sharpness in certain types of settings). Weighting the tripod can help in certain situations too. Oh yes, and ensuring you have not just a good 'tripod' (set of legs) but also the head is important, whether that be a ball head, 3 way, etc.... if you can, ensure you get a really good one. (good and well-looked after second hand items can be money better spent than full price new items). Just be sure to test everything you may buy 2nd hand prior to use.
I hope that you'll capture lots of good (sharp, and non-vibration affected) images in the future! Best wishes.
Best wishes,
PJ