@DaveMatthews: I have got a Lezyne CO2 Blaster repair kit, similar to yours. Only I have never had to use it
Now, anyone of you who could fix the tubeless with a spare tube: please tell me how you do it, starting from how you remove the tubeless valve, exactly?
it's just messy and time consuming. and as you have experienced virtually never necessary. but here is the process :
remove the wheel from the bike. if your through axles have levers, no tools required, if not, you'll need the 6mm hex key, which any multitool has.
remove the tire from the wheel using a tire lever.
unscrew the knurled nut on the exterior surface of the rim / tubeless valve.
if the valve is sticky, remove the valve core with the valve core tool. (i don't use caps on my valves but there are caps that have the tool built in)
push down on the valve from the center side and it will probably fall right out. if not, put something hard on it (with the valve core removed!!!) and use both thumbs with fingers around the rim.
put the tube in. partially inflate.
put the tire on. use the tire lever to seat both sides of the tire.
inflate and put back on the bike.
so, tool wise, it doesn't really require anything much more than repairing a bad tubed flat... but again, nobody should have to do this often. in my case, never, but i did it at home in my early tubeless days when i couldn't get a tire to hold air above 40psi for reasons unknown.