I have some chairs and some saddle stools I recently got for my work and they are a bit short, I don’t want to have to replace the gas cylinders or the chairs themselves. I thought about an extension sleeve that could go under the gas cylinder but after hours of searching was only able to find one example. Are there any other options to get them around 5-10inches taller?

Roller blade wheels are the easiest way
Not a chair expert but maybe you can find a higher base but 10inch probably a bit of a stretch...
I’d like to avoid having to replace parts, I might try to see if I can find some exhaust pipe and then have it stretched out the make an extension.
If you don't need it a ton taller, you could look up roller blade style caster wheels as they increase the height of chairs, plus they are just better wheels overall.
Other than that, as long as it doesn't adversely affect back ergonomics, you could also use memory foam seating pads. Types made for car seats and office chairs are pretty thick.
10 inch is too much. I'd get a drafting chair for high heights.
For many office chairs from China there are bar stool options that are much taller - for bank tellers and the like (customer is meanwhile standing). It will be a different base also with a circular metal footrest.