"Good morning, Grandmother."
Generally speaking, when referring to your grandmother and talking to someone else (specifically outside your family), you would use 祖母 (this applies to other words like 祖父、兄、母、子供、etc. as well). This is to humble oneself before the one they are speaking with by making the members of one's family (part of one's in-group) seem less "important" so to speak, which is a way of showing respect. There are situations where this is not the case but you shouldn't need to worry about those much yet. However, when talking directly to your own grandmother, you may want to use おばあさん/お祖母さん to show respect to her, as she is the one you are speaking with so you wouldn't need to humble your in-group for her since she's apart of it, in fact it may come off as rude to call her 祖母. To refer to her affectionately I read a comment that said ばば (like grandma/gram/nan I think) may be used instead? But don't quote me on that.
Interesting to learn that the 祖母 kanji can be used to write おばあさん, but note that, at least per Jisho, the word is normally written using kana: https://jisho.org/search/%E3%81%8A%E7%A5%96%E6%AF%8D%E3%81%95%E3%82%93
... I also read somewhere else that そぼ is used when talking about one's grandmother to someone not in the family, which answers my own question asked previously here, regarding why it couldn't be used.
But it doesn't accept it, despite it accepting お祖父ちゃん for grandfather. To be clear, it doesn't accept お祖母ちゃん、おはよう or おはよう , お祖母ちゃん but it does accept お祖母さん、おはよう! (from what I've observed the ちゃん suffix is used with grandparents more often than さん, though I guess it would depend on the family)
Shame you think that way, and it's sad today's generation are being brought up like this. If you ever meet with a Japanese family though, you need to get out of that Western mindset. At the Japanese functions I have attended, there is much respect shown to the grandparents, including addressing them properly. Even in death, relatives will show respect by visiting their graves on Grandparents Day (in September I think) even if it means travelling some distance back to their town.
If you were that knowledgeable about Japanese culture, you would understand that respect=/formality. If anything, formality=distance, and the Japanese are very aware of this. They'll adjust their formality depending on the person or context, otherwise it comes across as cold.