Progressive and continuous in Cantonese are different.
我著緊衫。-> I am wearing cloth.
You have not yet worn your clothes, and you try to do so, this is progressive, so you use 緊。
我著住(件)衫。-> I am wearing cloth.
You have already worn your clothes, but you still want to wear it(keeping the status), this is continuous, so you use 住。
"我食緊花生" v.s. "我食住花生睇戲"
For "我食住花生睇戲", eating could be treated as progressive, because the amount of food you have is changing, and not continuous because it does not involve a status change.
But you also express the word "while", and this is an exception which 住 is used instead. So you can have "我食住花生睇戲", but never "我食住花生". Some native speakers may use "我食緊花生睇戲".
So conclusion: 緊 for progressive, 住 for continuous OR (progressive + "while" meaning)
Example when 住 is not used:
This one is definitely progressive, since there are changes on the action during the progress(location change). People seldom use this to have "while" actions, so the conclusion, 住 is seldom used.
But you can have 唔去住, 唔嚟住, because there will not be changes if you DON'T go or DON'T come.
Example when 緊 cannot be used:
One cannot be dying as one could either be dead or alive, there is no progressing status between. So you cannot have "progress".
But you will still see the word 死緊，as in 我死緊份報告出嚟(a very rude expression). That is because here 死 here does not mean "die", but meaning "working one's best (with negative feelings) to do", and this meaning could exist as progressive form.
You have mentioned 梗 in your post. But actually this means "surely", and is put after verbs.
That's why you will see smth like 死梗，but the meaning will be "We are (surely) dead!"