Glaucoma can develop at any time. Glaucoma runs in my family, although I do not have it (yet) that means that I am entitled to annual eye tests to test for it.
Three years between eye tests is a long time, especially in old age, for all kinds of reasons. The recommended gap is two years and yes, you can easily develop glaucoma and have it quite badly in three years.
Cataracts, on the other hand can be quite slow developing and it may be, that it is not your glaucoma that is causing the delay in the operation but that the catatract is developing slowly and, at present, there is no need to operate.
I had a gap of about 5 years between the developing cataract in one eye being identified and the need for an operation to deal with it. My surgeons definition of 'needing' the operation was 'when the loss of clarity in my vision began to cause me troubles in my everyday life.
Like you I am/was severely short sighted, over -8 in one eye. One of the advantages of cataract operations is that you can have a new lens fitted which is made to your glasses prescription. After a life time of reaching out for my glasses first thing every morning, I no longer wear glasses, except for driving and distance viewing. Again that was a choice. I was told that I could have my prescription set up so I needed glasses for reading or distance - I made the distance choice.