If you're positive you don't have aphids or whitefly (both should be visible), then it's most likely thrips. Much smaller, almost microscopic. The white bits are discarded exoskeletons. The pale scratch markings on the leaves and the stickiness are both evidence of sap sucking insects. The stickiness is the characteristic excretion of honeydew. Here is info
https://ipm.ucanr.edu/PMG/PEST....
And another about pests in general
https://hgic.clemson.edu/facts...
I recall a conversation about this indoor impatiens a few months back, with the same issues. Most every respondent emphasized that these are plants better suited to outdoors and gave you suggestions for propagating new healthy plants. Their continued poor health suggests that they are not happy in their environment. The applications of various 'cides and chemicals have further debilitated them. Weakened, unhealthy plants are especially vulnerable to insect attacks and lack the resources to fight them. How might you combat the thrips? Least harmful is just washing the plant with water. Next step is insecticidal soap, but your plant is so fragile I'm reluctant to recommend more applications of anything.
I'm so sorry, I know you explained that this plant holds sentimental value. But you are trying to grow a plant unsuited to your situation. Yes, originally it bloomed profusely; it was young, fresh from the nursery with lots of fertilizer in the soil, and it lived for several months on its innate reserves. It has struggled for a long time and is very weak now.
I don't know what to suggest. I hope you can glean some helpful information from the articles.